C₂₃×#3142 #15670761

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3055
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#3142

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

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

normal subgroups only

This group has 392 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) = 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)(26,29)(27,28)(30,31)(32,33)(34,43)(35,38)(36,40)(37,42)(39,46)(41,44)(45,47);(25,28)(29,31)(32,34,44,45,37,46,36,35)(33,38,40,39,42,47,41,43);(24,26,27,30)(25,29,28,31)(32,35,36,46,37,45,44,34)(33,39,41,38,42,43,40,47);(32,36,37,44)(33,40,42,41)(34,45,46,35)(38,43,47,39)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9442, C₂₃×#10019, C₂₃×#10021, …
maximal normal subgroup of	C₂₃×#9442, C₂₃×#10019, C₂₃×#10021, …
maximal quotient of	C₂₃×#20765, C₂₃×#21093, C₂₃×#21201, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1874);