C₂₃×M₁₂₈ #15669047

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃×C₃₂ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₂₃×M₁₂₈

Subgroups

	subgroup	G/H
center	C₂₃×C₃₂	C₂²
commutator	C₂	C₂×C₂₃×C₃₂
Frattini, cosocle	C₃₂	C₂²×C₂₃
socle	C₂×C₂₃	C₂×C₃₂
prime radical	C₂²×C₂₃	C₃₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂₃×C₃₂ ◁ G

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 87
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 2 generators on 87 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87);(25,57)(27,59)(29,61)(31,63)(33,65)(35,67)(37,69)(39,71)(41,73)(43,75)(45,77)(47,79)(49,81)(51,83)(53,85)(55,87)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7511, C₂₃×#7513, C₂₃×#7514, …
maximal normal subgroup of	C₂₃×#7511, C₂₃×#7513, C₂₃×#7514, …
maximal quotient of	C₂₃×#7510, C₂₃×C₂²⋊C₆₄, C₂₃×C₄⋊C₆₄, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 160);

C23×M128 #15669047