C₂×#10677 #243942

order	512
nilpotency class	3
isoclinism	isoclinic class of #10304
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×#10677

Subgroups

	subgroup	G/H
center, socle	C₂⁴	#127
commutator, Frattini, cosocle	C₂×C₄²	C₂⁴
prime radical	C₂²×#127	C₂²
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁

1276 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 256

A minimal faithful permutation representation — 4 generators on 26 points:

(1,2);(3,4,6,8)(5,9,10,7)(11,12,13,17,15,18,14,16)(20,23)(24,25);(3,5,6,10)(4,7,8,9)(12,16)(13,14)(17,18)(19,20,21,23)(22,24,26,25);(12,17)(13,14)(16,18)(20,24)(22,26)(23,25)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#244406, #72216348
maximal normal subgroup of	C₂×#244406, #72216348
maximal quotient of	C₂×#117091

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 151138);

C2×#10677 #243942

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×#10677 #243942