C₂₃×#3255 #15670874

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

Aliases

direct product

C₂₃×#3255

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂³×C₂₃	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

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

normal subgroups only

This group has 342 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 47 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,28)(26,30)(32,33,37,40)(34,38,36,45)(35,42,44,46)(39,43,47,41);(24,25)(26,29)(27,28)(30,31)(32,34,37,36)(33,38,40,45)(35,43,44,41)(39,42,47,46);(25,28)(29,31)(32,35,37,44)(33,39,40,47)(34,41,36,43)(38,46,45,42);(24,26,27,30)(25,29,28,31)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#10113, C₂₃×#10115, C₂₃×#10117, …
maximal normal subgroup of	C₂₃×#10113, C₂₃×#10115, C₂₃×#10117, …
maximal quotient of	C₂₃×#21894, C₂₃×#21964, C₂₃×#22118, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1987);