C₂₃×#1923 #15669542

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₃×#1923

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₃	C₂³
commutator	C₂²	C₂²×C₈×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂³×C₂₃	C₂²×C₄
prime radical	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ G

292 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 39
transitive degree	μ_t(G) = 1472

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)(29,30)(32,33,35,38,36,34,37,39);(28,29,31,30)(32,34,35,39,36,33,37,38);(25,27)(28,30,31,29)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₃×#1923, C₂₃×#21046, C₂₃×#21048, …
maximal normal subgroup of	C₂×C₂₃×#1923, C₂₃×#21046, C₂₃×#21048, …
maximal quotient of	C₂₃×#9541, C₂₃×#9542, C₂₃×#9543, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 655);

C23×#1923 #15669542