C₂₃×#1453 #15669072

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₈

Aliases

direct product

C₂₃×#1453

Subgroups

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

190 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)(24,25,27,31,29,30,28,26)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(24,26,28,30,29,31,27,25)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(25,30)(26,31)(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×#7226, C₂₃×#11670, C₂×C₂₃×#1453, …
maximal normal subgroup of	C₂₃×#7226, C₂₃×#11670, C₂×C₂₃×#1453, …
maximal quotient of	C₂₃×#7844, C₂₃×#7850, C₂₃×#8134, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 185);

C23×#1453 #15669072