C₂₃×#3293 #15670912

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3290
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3293

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ G

444 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 184 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

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

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12311, C₂₃×#12313, C₂₃×#12367, …
maximal normal subgroup of	C₂₃×#12311, C₂₃×#12313, C₂₃×#12367, …
maximal quotient of	C₂₃×#19887, C₂₃×#19894, C₂₃×#19902, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2025);