C₂×#10859 #353646

order	512
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

direct product

C₂×#10859

Subgroups

	subgroup	G/H
center	C₂³×C₄	C₂×D₄
commutator	C₂×C₄	C₂²×C₄²
Frattini, cosocle	C₂³×C₄	C₂⁴
socle	C₂⁴	C₄×D₄
prime radical	C₂⁵	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄ ◁ C₂⁴×C₈ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

2418 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 128

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#93386, #72213009, C₂×#475764, …
maximal normal subgroup of	C₂×#93386, #72213009, C₂×#475764, …
maximal quotient of	#72211357, C₂×#109018

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260842);

C2×#10859 #353646

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₂×#10859 #353646