C₂₃×#2853 #15670472

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#2853

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)(29,31)(30,34)(37,40)(38,42);(28,29,32,31)(30,33,34,35)(36,37)(38,41)(39,40)(42,43);(28,30)(29,33)(31,35)(32,34);(24,25)(26,27)(28,31,32,29)(30,35,34,33)(36,38,39,42)(37,41,40,43)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#24057, C₂₃×#24113, C₂₃×#34983, …
maximal normal subgroup of	C₂₃×#24057, C₂₃×#24113, C₂₃×#34983, …
maximal quotient of	C₂₃×#14684, C₂₃×#14695, C₂₃×#14696, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1585);