C₂₃×#3021 #15670640

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#3021

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

736 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 212 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) = 39
transitive degree	μ_t(G) = 368

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13353, C₂₃×#13354, C₂₃×#13360, …
maximal normal subgroup of	C₂₃×#13353, C₂₃×#13354, C₂₃×#13360, …
maximal quotient of	C₂₃×#18135, C₂₃×#18141, C₂₃×#18145, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1753);