C₂×C₂₃×#557 #15671095

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂×C₂₃×#557

Subgroups

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

1048 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 5 generators on 41 points:

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

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8374, C₂₃×#8390, C₂₃×#8392, …
maximal normal subgroup of	C₂₃×#8374, C₂₃×#8390, C₂₃×#8392, …
maximal quotient of	C₂×Q₈×C₄⋊C₄×C₂₃, C₂×C₂₃×#2351, C₂×C₂₃×#2355, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2208);

C2×C23×#557 #15671095