C₂²×C₂₃×M₃₂ #15671024

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂²×C₂₃×M₃₂

Subgroups

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

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 43 points:

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

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#12544, C₂₃×#12545, C₂×C₂₃×#1375, …
maximal normal subgroup of	C₂₃×#12544, C₂₃×#12545, C₂×C₂₃×#1375, …
maximal quotient of	C₂²×C₂₃×#346, C₂×C₄×C₂₃×M₃₂, C₂²×C₂₃×C₂²⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2137);

C22×C23×M32 #15671024