C₂₃×#1454 #15669073

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₃×#1454

Subgroups

	subgroup	G/H
center	C₄²×C₂₃	C₂³
commutator	C₂²	C₂×C₄²×C₂₃
Frattini, cosocle	C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₄²
prime radical	C₂³×C₂₃	C₄²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₄²×C₂₃ ◁ G

178 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 55 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,31,28,30,34,37)(26,29,33,35,32,36,38,39)(40,41)(42,45)(43,47)(44,46)(48,52)(49,51)(50,53)(54,55);(24,26)(25,29)(27,33)(28,32)(30,36)(31,35)(34,38)(37,39)(40,42,43,48,44,49,50,54)(41,45,47,52,46,51,53,55);(25,30)(26,32)(31,37)(33,38)(41,46)(45,51)(47,53)(52,55)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₃×#1454, C₂₃×#17324, C₂₃×#17326, …
maximal normal subgroup of	C₂×C₂₃×#1454, C₂₃×#17324, C₂₃×#17326, …
maximal quotient of	C₂₃×#7845, C₂₃×#7851, C₂₃×#8135, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 186);

C23×#1454 #15669073