C₂₃×#3292 #15670911

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3290
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3292

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×C₄×C₂₃ ◁ G

476 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 184 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)(26,37)(27,33)(28,35)(29,34)(30,36)(31,38)(32,39);(24,26,30,32)(25,31,36,27)(28,33,29,38)(34,39,35,37);(24,27)(25,32)(26,36)(28,39)(29,37)(30,31)(33,34)(35,38);(24,27)(25,33)(26,35)(28,37)(29,39)(30,31)(32,34)(36,38)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12310, C₂₃×#12312, C₂₃×#12366, …
maximal normal subgroup of	C₂₃×#12310, C₂₃×#12312, C₂₃×#12366, …
maximal quotient of	C₂₃×#19885, C₂₃×#19893, C₂₃×#19898, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2024);