C₂×C₂₃×#518 #15671044

order	2944
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁹

Aliases

direct product

C₂×C₂₃×#518

Subgroups

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂⁴
commutator	C₂	C₂⁴×C₄×C₂₃
Frattini, cosocle	C₂²	C₂⁵×C₂₃
prime radical	C₂³×D₄×C₂₃	C₂
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

1920 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 5 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)(9,13)(10,11)(12,14);(8,11)(12,13);(7,8)(9,12)(10,11)(13,14);(7,9)(8,12)(10,14)(11,13)

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8322, C₂₃×#10740, C₂₃×#10745, …
maximal normal subgroup of	C₂₃×#8322, C₂₃×#10740, C₂₃×#10745, …
maximal quotient of	C₂×C₂₃×#2273, C₂×C₂₃×#2274, C₂×C₂₃×#2275, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2157);

C2×C23×#518 #15671044