C₂₃×#2356 #15669975

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#2356

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

464 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2944

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

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8768, C₂₃×#8769, C₂₃×#8774, …
maximal normal subgroup of	C₂₃×#8768, C₂₃×#8769, C₂₃×#8774, …
maximal quotient of	C₂₃×#13804, C₂₃×#13806, C₂₃×#13810, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1088);

C23×#2356 #15669975