#38763946

order	25422
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₁

Aliases

No aliases for this group.

Splittings

Fitting, socle, derived, Hall	C₁₉×C₂₂₃ ⋊ C₂×C₃
Hall	#27163278 ⋊ C₂
Hall	D₄₂₃₇ ⋊ C₃
Sylow	C₂₂₃ ⋊ D₁₉⋊C₃
Sylow	C₁₉ ⋊ D₂₂₃⋊C₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₉×C₂₂₃	C₂×C₃
LCS	G ▷ C₁₉×C₂₂₃
UCS	C₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 242
transitive degree	μ_t(G) = 4237

A minimal faithful permutation representation — 2 generators on 242 points:

(2,6,7,3,4,8)(5,14,15,9,10,24)(11,27,28,17,18,41)(12,26,22,20,16,13)(19,46,47,30,31,64)(21,44,45,33,29,38)(23,25,43,35,36,39)(32,69,70,49,50,93)(34,67,68,52,48,61)(37,42,66,54,55,62)(40,82,80,58,59,57)(51,98,99,72,73,128)(53,96,97,75,71,90)(56,65,95,77,78,91)(60,111,112,83,84,86)(63,117,109,87,88,81)(74,133,134,101,102,169)(76,131,132,104,100,125)(79,94,130,106,107,126)(85,146,147,113,114,121)(89,153,151,118,119,116)(92,158,144,122,123,110)(103,174,175,136,137,207)(105,172,173,139,135,166)(108,129,171,141,142,167)(115,185,186,148,149,162)(120,192,193,154,155,157)(124,197,190,159,160,152)(127,200,183,163,164,145)(138,203,184,168,177,214)(140,210,211,178,176,204)(143,170,209,180,181,205)(150,216,217,187,188,202)(156,220,221,194,195,199)(161,218,222,189,198,196)(165,212,219,179,201,191)(182,208,215,206,213,223)(225,229,230,226,227,231)(228,237,234,232,233,239)(235,240,242,241,238,236);(1,2,5,11,19,32,51,74,103,138,142,73,100,114,119,123,126,128,166,202,221,186,132,70,95,117,111,96,69,94,127,165,178,139,104,75,52,33,20,4,8,13,23,37,56,79,108,143,182,181,102,135,149,155,160,164,167,169,204,222,193,147,97,47,66,82,67,46,65,92,124,161,187,148,113,83,58,36,10,16,24,38,57,81,110,145,184,215,213,137,176,188,195,198,201,203,205,207,219,190,151,112,68,28,43,44,27,42,63,89,120,156,194,154,118,87,55,18,29,39,41,61,86,116,152,191,175,209,177,212,218,220,216,210,174,208,223,214,183,144,109,80,45,15,26,14,25,40,60,85,115,150,189,159,122,78,31,48,59,62,64,90,121,157,196,211,134,171,200,197,192,185,172,133,170,206,180,141,106,77,54,35,22,7,6,12,21,34,53,76,105,140,179,163,107,50,71,84,88,91,93,125,162,199,217,173,99,130,158,153,146,131,98,129,168,136,101,72,49,30,17,9,3)(224,225,228,234,240,237,241,227,231,236,242,230,229,235,233,238,239,232,226)

Polycyclic presentation:

2,3,19,223|c^a=c^18,d^a=d^222,c^b=c^7,d^b=d^39

Conjugacy classes & character table

712 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25422, 24);