C₂₃×#2888 #15670507

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2883
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#2888

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×H(5,𝔽₂)	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×#41×C₂₃ ◁ G

756 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 756 conjugacy classes of subgroups — too many to draw. Only its 340 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)(24,25,27,31,28,29,34,36)(26,30,33,37,32,35,38,39);(25,29)(27,34)(30,35)(33,38);(24,26)(25,30)(27,33)(28,32)(29,35)(31,37)(34,38)(36,39);(26,32)(30,35)(33,38)(37,39)

Conjugacy classes & character table

943 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13097, C₂₃×#13099, C₂₃×#21778, …
maximal normal subgroup of	C₂₃×#13097, C₂₃×#13099, C₂₃×#21778, …
maximal quotient of	C₂₃×#17350, C₂₃×#17353, C₂₃×#17367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1620);