C₂₃×#2556 #15670175

order	2944
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2556

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂⁴×C₂₃	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

492 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(29,32)(33,35)(36,37,40,38)(39,42,43,41);(24,25,26,27)(37,38)(41,42);(24,25)(26,27)(28,29)(30,33)(31,32)(34,35)(36,38,40,37)(39,42,43,41);(28,30,31,34)(29,33,32,35)(36,39)(37,41)(38,42)(40,43)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₂₃×#2556, C₂₃×#34829, C₂₃×#34840, …
maximal normal subgroup of	C₂×C₂₃×#2556, C₂₃×#34829, C₂₃×#34840, …
maximal quotient of	C₂₃×#13915, C₂₃×#13930, C₂₃×#14009, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1288);

C23×#2556 #15670175

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂₃×#2556 #15670175