C₂₃×#1971 #15669590

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

Aliases

direct product

C₂₃×#1971

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

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

normal subgroups only

This group has 304 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)(34,42)(35,38)(36,45)(37,41)(39,43)(40,46)(44,47);(24,25,26,27)(29,31)(32,34,36,35,37,43,46,44)(33,38,40,42,41,47,45,39);(32,35,36,43,37,44,46,34)(33,39,40,38,41,42,45,47)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7111, C₂₃×#13026, C₂₃×#13039, …
maximal normal subgroup of	C₂₃×#7111, C₂₃×#13026, C₂₃×#13039, …
maximal quotient of	C₂₃×#9658, C₂₃×#9664, C₂₃×#9720, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 703);