C₂²×#19098457 #34446599

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄ · Schur multiplier (H₂) = C₂⁹×C₄

Aliases

direct product

C₂²×#19098457

Splittings

Sylow

C₇₉ ⋊ C₂²×#388

Subgroups

	subgroup	G/H
center	C₂⁵	C₂²×D₇₉
commutator	C₂²×C₇₉	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₇₉
Fitting	C₂³×C₂²⋊C₄×C₇₉	C₂
socle	C₂⁵×C₇₉	C₂³
prime radical	C₂⁶×C₇₉	C₂²
cosocle	C₂³×C₇₉	C₂⁵
hypercenter	C₂³×C₂²⋊C₄	D₇₉
hypocenter	C₇₉	C₂²×#388
LCS	G ▷ C₂²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂⁵ ◁ C₂³×C₂²⋊C₄

5966 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 95
transitive degree	μ_t(G) = 10112

A minimal faithful permutation representation — 5 generators on 95 points:

(10,12)(13,15,16,14)(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);(5,7,8,6)(13,14,16,15)(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);(5,6,8,7)(9,10)(11,12)(14,15)(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);(3,4);(1,2)

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 327898);

C22×#19098457 #34446599