C₂₃×#1960 #15669579

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

Aliases

direct product

C₂₃×#1960

Subgroups

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

308 conjugacy classes of subgroups; only the 128 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 128 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)(25,27)(28,29,30,31)(32,33)(34,40)(35,43)(36,38)(37,42)(39,44)(41,46)(45,47);(29,31)(32,34,35,42,36,41,44,47)(33,37,39,40,38,45,43,46);(24,25,26,27)(33,38)(34,41)(39,43)(42,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7117, C₂₃×#7353, C₂₃×#7505, …
maximal normal subgroup of	C₂₃×#7117, C₂₃×#7353, C₂₃×#7505, …
maximal quotient of	C₂₃×#9641, C₂₃×#9647, C₂₃×#9683, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 692);