C₂₃×#1533 #15669152

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1510
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1533

Subgroups

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

248 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 88 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) = 736

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)(24,25,26,29,27,28,30,31)(32,33)(34,40,42,47)(35,39)(36,38)(37,41,45,43)(44,46);(25,28)(26,30)(32,34)(33,37)(35,43)(36,42)(38,45)(39,47)(40,46)(41,44);(33,38)(37,45)(39,46)(40,47)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7481, C₂₃×#7495, C₂₃×#8522, …
maximal normal subgroup of	C₂₃×#7481, C₂₃×#7495, C₂₃×#8522, …
maximal quotient of	C₂₃×#7592, C₂₃×#7595, C₂₃×#7601, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 265);