C₄×C₂₃×#131 #15670493

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₄×C₂₃×#131

Subgroups

	subgroup	G/H
center	C₄×C₈×C₂₃	C₂²
commutator	C₂	C₂²×C₄²×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₈×C₂₃ ◁ G

572 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:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#8184, C₂₃×#8185, C₂₃×#8186, …
maximal normal subgroup of	C₂₃×#8184, C₂₃×#8185, C₂₃×#8186, …
maximal quotient of	C₈×C₂₃×#131, C₂₃×#17320, C₂₃×#17328, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1606);

C4×C23×#131 #15670493