C₂²×#19098350 #34440980

order	20224
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₂²×#19098350

Splittings

Sylow

C₇₉ ⋊ C₂²×AΣL(1,𝔽₁₆)

Subgroups

	subgroup	G/H
center	C₂³	#14579076
commutator	C₂³×C₇₉	C₂³×C₄
Frattini	C₂×D₄	C₂³×D₇₉
Fitting, prime radical	C₂²×#120×C₇₉	C₂
socle	C₂³×C₇₉	#99
cosocle	C₂×D₄×C₇₉	C₂⁴
hypercenter	C₂²×#120	D₇₉
hypocenter	C₇₉	C₂²×AΣL(1,𝔽₁₆)
LCS	G ▷ C₂³×C₇₉ ▷ C₂²×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂⁴ ◁ C₂³×D₄ ◁ C₂²×#120

2774 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 91
transitive degree	μ_t(G) = 2528

A minimal faithful permutation representation — 4 generators on 91 points:

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

Conjugacy classes & character table

2236 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 322279);

C22×#19098350 #34440980