Finite Group Databasebeta

← Prev (#6466039) Next (#6466041) →

Cayley diagram

C2×#28291 #6466040

order512
nilpotency class3
isoclinismisoclinic class of #23924
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#28291

Subgroups

subgroupG/H
center, socle, prime radicalC24C22×D4
commutator, Frattini, cosocleC22×C4C25
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×#376 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

2130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 512

A minimal faithful permutation representation — 5 generators on 30 points:

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6373236);