C₂₃×#1528 #15669147

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1528

Subgroups

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

212 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 92 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)(25,28,29,30)(32,33,35,39,36,38,44,46)(34,40,41,47,42,37,43,45);(24,25)(26,30)(27,29)(28,31)(32,34,36,42)(33,37,38,40)(35,43,44,41)(39,47,46,45);(33,38)(37,40)(39,46)(45,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8371, C₂₃×#8372, C₂₃×#8373, …
maximal normal subgroup of	C₂₃×#8371, C₂₃×#8372, C₂₃×#8373, …
maximal quotient of	C₂₃×#7573, C₂₃×#7576, C₂₃×#7585, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 260);