C₂₃×#3026 #15670645

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3026
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#3026

Subgroups

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

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

normal subgroups only

This group has 800 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)(24,25)(26,29)(27,30)(28,31)(32,38)(33,36)(34,37)(35,39);(24,26)(25,29)(27,32)(28,33)(30,35)(31,36)(34,39)(37,38);(24,27)(25,30)(26,32)(28,34)(29,35)(31,37)(33,39)(36,38);(25,31)(29,36)(30,37)(35,38)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#23895, C₂₃×#23896, C₂₃×#23996, …
maximal normal subgroup of	C₂₃×#23895, C₂₃×#23896, C₂₃×#23996, …
maximal quotient of	C₂₃×#18284, C₂₃×#18285, C₂₃×#18286, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1758);