C₂₃×#1839 #15669458

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

Aliases

direct product

C₂₃×#1839

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

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 47
transitive degree	μ_t(G) = 2944

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7019, C₂₃×#7023, C₂₃×#7041, …
maximal normal subgroup of	C₂₃×#7019, C₂₃×#7023, C₂₃×#7041, …
maximal quotient of	C₂₃×#8800, C₂₃×#8801, C₂₃×#10795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 571);

C23×#1839 #15669458