Finite Group Databasebeta

← Prev (#6466173) Next (#6466175) →

Cayley diagram

C2×#28544 #6466174

order512
nilpotency class3
isoclinismisoclinic class of #24274
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#28544

Subgroups

subgroupG/H
center, socleC24C22×D4
commutator, Frattini, cosocleC22×C4C25
prime radicalC23×D8C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4 ◁ G
LECSG ▷ C22×C4 ▷ C2 ▷ C1

2630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 30
transitive degreeμt(G) = 256

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

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

Conjugacy classes & character table

92 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#6466187, C2×#6574618, C2×#6577964
maximal normal subgroup ofC2×#6466187, C2×#6574618, C2×#6577964

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 6373370);