C₂₃×#1967 #15669586

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₃×#1967

Subgroups

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

312 conjugacy classes of subgroups; only the 112 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 112 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) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 43 points:

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8483, C₂₃×#8484, C₂₃×#10496, …
maximal normal subgroup of	C₂₃×#8483, C₂₃×#8484, C₂₃×#10496, …
maximal quotient of	C₂₃×#9651, C₂₃×#9652, C₂₃×#9687, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 699);