Finite Group Databasebeta

← Prev (#499147) Next (#499149) →

Cayley diagram

C2×#13433 #499148

order512
nilpotency class4
isoclinismisoclinic class of #13432
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#13433

Subgroups

subgroupG/H
center, socleC22#2044
commutator, Frattini, cosocleC2×#41C24
prime radicalC2×#535C22
LCSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×#41 ◁ G
LECSG ▷ C2×#41 ▷ C22 ▷ C2 ▷ C1

1125 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);(4,9)(5,13)(6,17)(7,20)(10,24)(11,26)(12,18)(14,30)(15,32)(16,29)(21,23)(22,25)(27,31)(28,33);(3,4,8,12)(5,14,16,10)(6,18,17,9)(7,21,20,11)(13,27,29,25)(15,22,33,31)(19,23,34,26)(24,32,30,28);(3,5,6,15,8,16,17,33)(4,10,9,22,12,14,18,31)(7,13,19,28,20,29,34,32)(11,25,23,24,21,27,26,30)

Conjugacy classes & character table

56 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#72312842, #72312855, C2×#501196, …
maximal normal subgroup of#72312842, #72312855, C2×#501196, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 406344);