C₂₃×#2150 #15669769

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

Aliases

direct product

C₂₃×#2150

Subgroups

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

172 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29,30,34,31,35,36,41,32,33,37,39,38,40,42,43);(24,25,26,27);(29,33)(34,39)(35,40)(41,43)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7152, C₂₃×#7153, C₂₃×#7168, …
maximal normal subgroup of	C₂₃×#7152, C₂₃×#7153, C₂₃×#7168, …
maximal quotient of	C₂₃×#11996, C₂₃×#12004, C₂₃×#12013, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 882);

C23×#2150 #15669769