C₂₃×#2883 #15670502

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×#2883

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂×C₂₃×H(5,𝔽₂)	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×D₄×C₂₃ ◁ G

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

normal subgroups only

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

Conjugacy classes & character table

943 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13100, C₂₃×#13102, C₂₃×#21776, …
maximal normal subgroup of	C₂₃×#13100, C₂₃×#13102, C₂₃×#21776, …
maximal quotient of	C₂₃×#17350, C₂₃×#17351, C₂₃×#17367, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1615);