C₂₃×#2852 #15670471

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2852

Subgroups

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

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

normal subgroups only

This group has 582 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) = 43
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 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)(29,32)(30,34)(37,41)(39,43);(28,29)(30,33)(31,32)(34,35)(36,37,40,41)(38,39,42,43);(28,30,31,34)(29,33,32,35)(36,38,40,42)(37,39,41,43);(24,25)(26,27)(28,29)(30,33)(31,32)(34,35)(36,39)(37,42)(38,41)(40,43)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#34990, C₂₃×#34991, C₂₃×#34995, …
maximal normal subgroup of	C₂₃×#34990, C₂₃×#34991, C₂₃×#34995, …
maximal quotient of	C₂₃×#14683, C₂₃×#14695, C₂₃×#14696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1584);