C₂₃×#1798 #15669417

order	2944
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1798

Subgroups

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

312 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 136 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 — 3 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)(25,27)(28,29)(30,31)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(24,25,26,27)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(29,31)(34,40)(37,43)(41,46)(44,47)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7252, C₂₃×#7253, C₂₃×#8409, …
maximal normal subgroup of	C₂₃×#7252, C₂₃×#7253, C₂₃×#8409, …
maximal quotient of	C₂₃×#8561, C₂₃×#8562, C₂₃×#8567, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 530);