C₂₃×#1764 #15669383

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₂₃×#1764

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₃	D₄
commutator	C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₄×D₄
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

300 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 43 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)(28,29,32,36,33,37,31,34)(30,35,39,42,40,43,38,41);(25,27)(29,34,37,36)(35,41,43,42);(28,30,32,39,33,40,31,38)(29,35,36,42,37,43,34,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#12614, C₂₃×#12615, C₂₃×#12917, …
maximal normal subgroup of	C₂₃×#12614, C₂₃×#12615, C₂₃×#12917, …
maximal quotient of	C₂₃×#8184, C₂₃×#8186, C₂₃×#8187, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 496);

C23×#1764 #15669383