C₂×#23769138 #34454603

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁵ · Schur multiplier (H₂) = C₂⁸×C₄

Aliases

direct product

C₂×#23769138

Splittings

Fitting	C₂²×#120×C₇₉ ⋊ C₂
Sylow	C₇₉ ⋊ C₂×#2617

Subgroups

	subgroup	G/H
center	C₂⁴	C₂³×D₇₉
commutator, cosocle	C₂³×C₇₉	C₂⁵
Frattini	C₂³	C₂⁴×D₇₉
Fitting	C₂²×#120×C₇₉	C₂
socle	C₂⁴×C₇₉	C₂⁴
hypercenter	C₂²×#120	D₇₉
hypocenter	C₇₉	C₂×#2617
LCS	G ▷ C₂³×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁴ ◁ C₂²×#120

5222 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 97
transitive degree	μ_t(G) = 5056

A minimal faithful permutation representation — 5 generators on 97 points:

(13,17)(16,18)(19,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21);(4,6)(8,10)(11,13)(12,16)(14,17)(15,18);(7,8)(9,10)(12,15)(16,18);(3,4,5,6)(11,12)(13,16)(14,15)(17,18)(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);(1,2)

Conjugacy classes & character table

2248 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 335902);

C2×#23769138 #34454603