Finite Group Databasebeta

← Prev (#6353964) Next (#6353966) →

Cayley diagram

C2×#19309 #6353965

order512
nilpotency class3
isoclinismisoclinic class of #19304
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19309

Subgroups

subgroupG/H
center, socleC23C2×#121
commutator, Frattini, cosocleC42C25
prime radicalC2×#532C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C23 ◁ C22×C42 ◁ G
LECSG ▷ C42 ▷ C22 ▷ C1

1716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 34
transitive degreeμt(G) = 256

A minimal faithful permutation representation — 5 generators on 34 points:

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

Conjugacy classes & character table

74 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#6363073, C2×#6363065, C2×#6354109
maximal normal subgroup ofC2×#6363073, C2×#6363065, C2×#6354109

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6261161);