D₁₂₉₄₇ #39905916

order	25894
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₂₉₄₇
unambiguous semidirect product	C₁₀₇⋊D₁₂₁
unambiguous semidirect product	C₁₂₁⋊D₁₀₇

Splittings

Fitting, derived, Hall	C₁₀₇×C₁₂₁ ⋊ C₂
Sylow	C₁₂₁ ⋊ D₁₀₇
Sylow	C₁₀₇ ⋊ D₁₂₁

Subgroups

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₁₀₇×C₁₂₁	C₂
Frattini	C₁₁	D₁₁₇₇
socle	C₁₁×C₁₀₇	D₁₁
LCS	G ▷ C₁₀₇×C₁₂₁
UCS	C₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 228
transitive degree	μ_t(G) = 12947

A minimal faithful permutation representation — 2 generators on 228 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121)(122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181,182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224,225,226,227,228);(2,121)(3,120)(4,119)(5,118)(6,117)(7,116)(8,115)(9,114)(10,113)(11,112)(12,111)(13,110)(14,109)(15,108)(16,107)(17,106)(18,105)(19,104)(20,103)(21,102)(22,101)(23,100)(24,99)(25,98)(26,97)(27,96)(28,95)(29,94)(30,93)(31,92)(32,91)(33,90)(34,89)(35,88)(36,87)(37,86)(38,85)(39,84)(40,83)(41,82)(42,81)(43,80)(44,79)(45,78)(46,77)(47,76)(48,75)(49,74)(50,73)(51,72)(52,71)(53,70)(54,69)(55,68)(56,67)(57,66)(58,65)(59,64)(60,63)(61,62)(123,228)(124,227)(125,226)(126,225)(127,224)(128,223)(129,222)(130,221)(131,220)(132,219)(133,218)(134,217)(135,216)(136,215)(137,214)(138,213)(139,212)(140,211)(141,210)(142,209)(143,208)(144,207)(145,206)(146,205)(147,204)(148,203)(149,202)(150,201)(151,200)(152,199)(153,198)(154,197)(155,196)(156,195)(157,194)(158,193)(159,192)(160,191)(161,190)(162,189)(163,188)(164,187)(165,186)(166,185)(167,184)(168,183)(169,182)(170,181)(171,180)(172,179)(173,178)(174,177)(175,176)

Polycyclic presentation:

2,11,107,11|b^11=d^10,b^a=b^10d,c^a=c^106,d^a=d^10

Conjugacy classes & character table

6475 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₂₉₄₇
maximal normal subgroup of	C₂×D₁₂₉₄₇
maximal quotient of	Dic₁₂₉₄₇, C₂×D₁₂₉₄₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25894, 4);

D12947 #39905916