C₂₃×#3407 #15671026

order	2944
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3407

Subgroups

	subgroup	G/H
center	C₈×C₂₃	C₂⁴
commutator	C₂	C₂³×C₈×C₂₃
Frattini, cosocle	C₈	C₂⁴×C₂₃
socle	C₂×C₂₃	C₂³×C₈
prime radical	C₂×#41×C₂₃	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₃ ◁ G

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 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)(24,25,27,32,28,33,37,45,29,31,38,43,39,44,49,53)(26,30,35,41,36,42,48,52,34,40,46,50,47,51,54,55);(24,26)(25,30)(27,35)(28,36)(29,34)(31,40)(32,41)(33,42)(37,48)(38,46)(39,47)(43,50)(44,51)(45,52)(49,54)(53,55);(26,34)(30,40)(35,46)(36,47)(41,50)(42,51)(48,54)(52,55);(25,31)(30,40)(32,43)(33,44)(41,50)(42,51)(45,53)(52,55)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#12618, C₂₃×#12833, C₂₃×#12915, …
maximal normal subgroup of	C₂₃×#12618, C₂₃×#12833, C₂₃×#12915, …
maximal quotient of	C₂₃×#33324, C₂₃×#33326, C₂₃×#33333, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2139);

C23×#3407 #15671026