C₂₃×#1397 #15669016

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₆×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#1397

Subgroups

	subgroup	G/H
center	C₂×C₁₆×C₂₃	C₂²
commutator	C₂	C₄×C₁₆×C₂₃
Frattini, cosocle	C₂×C₁₆	C₂²×C₂₃
socle, prime radical	C₂²×C₂₃	C₂×C₁₆
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₆×C₂₃ ◁ G

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 59
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 2 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(28,29,30,35,31,36,38,47,32,37,39,48,41,49,50,57,33,34,40,44,42,45,51,54,43,46,52,55,53,56,58,59);(24,25,26,27)(29,34)(35,44)(36,45)(37,46)(47,54)(48,55)(49,56)(57,59)

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7330, C₂₃×#7332, C₂₃×#7380, …
maximal normal subgroup of	C₂₃×#7330, C₂₃×#7332, C₂₃×#7380, …
maximal quotient of	C₂₃×#7329, C₂₃×#7331, C₂₃×#7465, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 129);

C23×#1397 #15669016