C₂₃×#2183 #15669802

order	2944
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₂₃×#2183

Subgroups

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

126 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)(32,33,35,39,36,34,41,42,37,40,44,47,45,43,38,46);(24,26,28,27)(25,29,30,31);(24,27,28,26)(25,29,30,31)(32,34,35,42,36,40,41,47,37,43,44,46,45,33,38,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7393, C₂₃×#12049, C₂₃×#12051, …
maximal normal subgroup of	C₂₃×#7393, C₂₃×#12049, C₂₃×#12051, …
maximal quotient of	C₂₃×#12662, C₂₃×#12663, C₂₃×#13104, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 915);

C23×#2183 #15669802