Finite Group Databasebeta

← Prev (#353128) Next (#353130) →

Cayley diagram

C2×#10701 #353129

order512
nilpotency class3
isoclinismisoclinic class of AGL(1,ℤ/8)
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C25×C42

Aliases

direct productC2×#10701

Subgroups

subgroupG/H
centerC23×C4C2×D4
commutatorC4C2×C43
Frattini, cosocleC23×C4C24
socleC24C2×C22⋊C4
prime radicalC25C2×D4
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C4 ◁ C23×C42 ◁ G
LECSG ▷ C23×C4 ▷ C2 ▷ C1

2962 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 128

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

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72213013, #72215774, C2×#379089, …
maximal normal subgroup of#72213013, #72215774, C2×#379089, …
maximal quotient of#72212990, #72303131

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 260325);