C₂×D₈₄₁₃ #46777813

order	33652
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₁₆₈₂₆
direct product	C₂×D₈₄₁₃
unambiguous semidirect product	(C₂×C₄₇)⋊D₁₇₉
unambiguous semidirect product	(C₂×C₁₇₉)⋊D₄₇

Splittings

Fitting, socle	C₂×C₄₇×C₁₇₉ ⋊ C₂
derived, Hall	C₄₇×C₁₇₉ ⋊ C₂²
Sylow	C₁₇₉ ⋊ C₂×D₄₇
Sylow	C₄₇ ⋊ C₂×D₁₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₈₄₁₃
commutator, cosocle, hypocenter	C₄₇×C₁₇₉	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₄₇×C₁₇₉	C₂
LCS	G ▷ C₄₇×C₁₇₉
UCS	C₁ ◁ C₂

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 228
transitive degree	μ_t(G) = 16826

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

Conjugacy classes & character table

8416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33652, 9);

C2×D8413 #46777813