C₂₃×#3166 #15670785

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#3166

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

348 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 216 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)(24,25,27,29)(26,30,31,28)(32,33,35,37)(34,40,41,47)(36,44,43,39)(38,46,45,42);(24,26,27,31)(25,28,29,30)(33,37)(38,45)(39,44)(40,47);(32,34,36,42,35,41,43,46)(33,38,39,40,37,45,44,47);(34,41)(38,45)(40,47)(42,46)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9440, C₂₃×#10023, C₂₃×#10025, …
maximal normal subgroup of	C₂₃×#9440, C₂₃×#10023, C₂₃×#10025, …
maximal quotient of	C₂₃×#20801, C₂₃×#21159, C₂₃×#21323, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1898);