C₂₃×#1450 #15669069

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₂₃ · Schur multiplier (H₂) = C₂×C₈

Aliases

direct product

C₂₃×#1450

Subgroups

	subgroup	G/H
center	C₄×C₈×C₂₃	C₂²
commutator	C₂	C₂×C₄×C₈×C₂₃
Frattini, cosocle	C₄²	C₂³×C₂₃
socle	C₂²×C₂₃	C₂×C₄²
prime radical	C₂³×C₂₃	C₄²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₂₃ ◁ G

212 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 1472

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)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(24,25,26,28,27,29,30,31)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(34,40)(37,43)(41,46)(44,47)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7140, C₂₃×#7141, C₂₃×#7153, …
maximal normal subgroup of	C₂₃×#7140, C₂₃×#7141, C₂₃×#7153, …
maximal quotient of	C₂₃×#7841, C₂₃×#7849, C₂₃×#8133, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 182);

C23×#1450 #15669069