C₂³×#41×C₂₃ #15671209

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₂₃ · Schur multiplier (H₂) = C₂¹⁴

Aliases

direct product

C₂³×#41×C₂₃

Subgroups

	subgroup	G/H
center	C₂³×C₄×C₂₃	C₂²
commutator, Frattini, cosocle	C₂	C₂⁶×C₂₃
socle	C₂⁴×C₂₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄×C₂₃ ◁ G

6520 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 6 generators on 37 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#13851, C₂₃×#13937, C₂₃×#13956, …
maximal normal subgroup of	C₂₃×#13851, C₂₃×#13937, C₂₃×#13956, …
maximal quotient of	C₂³×C₂₃×#117, C₂³×C₄×D₄×C₂₃, C₂³×C₄×Q₈×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2322);

C23×#41×C23 #15671209