C₂₃×#3573 #15671192

order	2944
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂₃×#3573

Subgroups

	subgroup	G/H
center	C₈×C₂₃	C₂⁴
commutator	C₂	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₄	C₂⁵×C₂₃
socle	C₂×C₂₃	C₂⁴×C₄
prime radical	C₂₃×#585	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₃ ◁ G

1424 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 5 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)(24,25,28,32,29,33,39,45)(26,30,36,42,35,41,48,52)(27,31,38,44,37,43,49,53)(34,40,47,51,46,50,54,55);(24,26)(25,30)(27,34)(28,36)(29,35)(31,40)(32,42)(33,41)(37,46)(38,47)(39,48)(43,50)(44,51)(45,52)(49,54)(53,55);(24,27)(25,31)(26,34)(28,38)(29,37)(30,40)(32,44)(33,43)(35,46)(36,47)(39,49)(41,50)(42,51)(45,53)(48,54)(52,55);(27,37)(31,43)(34,46)(38,49)(40,50)(44,53)(47,54)(51,55);(26,35)(30,41)(34,46)(36,48)(40,50)(42,52)(47,54)(51,55)

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#12684, C₂₃×#12685, C₂₃×#21477, …
maximal normal subgroup of	C₂₃×#12684, C₂₃×#12685, C₂₃×#21477, …
maximal quotient of	C₂₃×#60058, C₂₃×#60065, C₂₃×#60100, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2305);

C23×#3573 #15671192