C₂₃×#2901 #15670520

order	2944
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#2901

Subgroups

	subgroup	G/H
center	C₄×C₂₃	C₂²×D₄
commutator	C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂×C₂₃	C₂²×C₂²⋊C₄
prime radical	C₂₃×#585	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂×#41×C₂₃ ◁ G

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

normal subgroups only

This group has 738 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)(24,25,28,32,29,26,33,31)(27,30,36,38,35,34,39,37);(24,26)(25,29)(27,34)(28,31)(30,35)(32,33)(36,37)(38,39);(24,27)(25,30)(26,34)(28,36)(29,35)(31,37)(32,38)(33,39);(27,35)(30,34)(36,39)(37,38)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#22461, C₂₃×#22462, C₂₃×#22898, …
maximal normal subgroup of	C₂₃×#22461, C₂₃×#22462, C₂₃×#22898, …
maximal quotient of	C₂₃×#17438, C₂₃×#17439, C₂₃×#17453, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1633);