C₂₃×#2342 #15669961

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#2342

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂³	C₂⁴×C₂₃
prime radical	C₂⁵×C₂₃	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 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)(28,29,30,31)(32,33)(34,38)(35,37)(36,39);(25,27)(32,33,35,37)(34,36,39,38);(32,34)(33,36)(35,39)(37,38);(24,25)(26,27)(32,33)(34,36)(35,37)(38,39)

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#22405, C₂₃×#22477, C₂×C₂₃×#2342, …
maximal normal subgroup of	C₂₃×#22405, C₂₃×#22477, C₂×C₂₃×#2342, …
maximal quotient of	C₂²⋊C₄²×C₂₃, C₂₃×#13799, C₂₃×#13802, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1074);

C23×#2342 #15669961