C₂₃×#1467 #15669086

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1467

Subgroups

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

236 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 100 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)(24,25,27,29,28,30,26,31)(32,33)(34,40,42,37)(35,38)(36,39)(41,46,47,44)(43,45);(32,34,36,42)(33,37,39,40)(35,41,43,47)(38,44,45,46);(24,26,28,27)(25,29,30,31)(32,35,36,43)(33,38,39,45)(34,41,42,47)(37,44,40,46)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7248, C₂₃×#7323, C₂₃×#8368, …
maximal normal subgroup of	C₂₃×#7248, C₂₃×#7323, C₂₃×#8368, …
maximal quotient of	C₂₃×#7619, C₂₃×#7622, C₂₃×#7625, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 199);