C₂₃×#1939 #15669558

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1939

Subgroups

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

260 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 3 generators on 39 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)(29,31)(32,33,36,34,35,37,39,38);(25,27)(32,34,36,37,35,38,39,33);(28,29,30,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7118, C₂₃×#8843, C₂₃×#8844, …
maximal normal subgroup of	C₂₃×#7118, C₂₃×#8843, C₂₃×#8844, …
maximal quotient of	C₂₃×#9593, C₂₃×#9594, C₂₃×#9595, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 671);

C23×#1939 #15669558