C₂₃×#2640 #15670259

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2613
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂²×C₄²

Aliases

direct product

C₂₃×#2640

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂²×D₄×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

500 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 43
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27)(28,29,32,35)(30,31,34,33)(38,42)(40,43);(24,25,26,27)(28,30,32,34)(29,33,35,31)(36,37,39,41)(38,40,42,43);(24,25)(26,27)(28,30)(29,33)(31,35)(32,34)(36,38)(37,40)(39,42)(41,43);(28,31,32,33)(29,34,35,30)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10090, C₂₃×#10092, C₂₃×#10098, …
maximal normal subgroup of	C₂₃×#10090, C₂₃×#10092, C₂₃×#10098, …
maximal quotient of	C₂₃×#14260, C₂₃×#14261, C₂₃×#14273, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1372);