Finite Group Databasebeta

← Prev (#499210) Next (#499212) →

Cayley diagram

C2×#13460 #499211

order512
nilpotency class4
isoclinismisoclinic class of #13460
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#13460

Subgroups

subgroupG/H
center, socleC22#2058
commutator, Frattini, cosocleC22×C8C24
prime radicalC24C2×SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#405 ◁ G
LECSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1

790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 64

A minimal faithful permutation representation — 4 generators on 34 points:

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

Conjugacy classes & character table

68 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72231475, #72231484, C2×#499269, …
maximal normal subgroup of#72231475, #72231484, C2×#499269, …
maximal quotient of#72250189, #72251009, #72251042, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406407);