C₂₃×#2227 #15669846

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2184
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#2227

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

130 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 130 conjugacy classes of subgroups — too many to draw. Only its 68 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) = 2944

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

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12373, C₂₃×#12374, C₂₃×#12379, …
maximal normal subgroup of	C₂₃×#12373, C₂₃×#12374, C₂₃×#12379, …
maximal quotient of	C₂₃×#12812, C₂₃×#12936, C₂₃×#13112, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 959);