Finite Group Databasebeta

← Prev (#202482) Next (#202484) →

Cayley diagram

C2×#9552 #202483

order512
nilpotency class3
isoclinismisoclinic class of #2018
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#9552

Subgroups

subgroupG/H
centerC22×C4#121
commutatorC22×C4C23×C4
Frattini, cosocleC2×C42C24
socleC23#388
prime radicalC23×D4C2×C4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ G
LECSG ▷ C2×C42 ▷ C22 ▷ C1

932 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 128

A minimal faithful permutation representation — 4 generators on 26 points:

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

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#202513, #72215902, #72215911, …
maximal normal subgroup ofC2×#202513, #72215902, #72215911, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 109679);