C₂₃×#3192 #15670811

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3192
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#3192

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

514 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 736

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9343, C₂₃×#9930, C₂₃×#9932, …
maximal normal subgroup of	C₂₃×#9343, C₂₃×#9930, C₂₃×#9932, …
maximal quotient of	C₂₃×#21764, C₂₃×#21942, C₂₃×#22046, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1924);