C₂₃×#1729 #15669348

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#1729

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂³
commutator	C₂²	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂³×C₂₃	C₂²×C₄
prime radical	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

416 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)(24,25)(26,27)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(25,27)(28,29,30,31)(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

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7185, C₂₃×#7186, C₂₃×#7188, …
maximal normal subgroup of	C₂₃×#7185, C₂₃×#7186, C₂₃×#7188, …
maximal quotient of	C₂₃×#7848, C₂₃×#7849, C₂₃×#7850, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 461);

C23×#1729 #15669348