Finite Group Databasebeta

← Prev (#91317) Next (#91319) →

Cayley diagram

C2×#6661 #91318

order480
isoclinismisoclinic class of #6652
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#6661

Splittings

HallC3×C5 ⋊ C2×Q16
SylowC5 ⋊ C2×#216
SylowC3 ⋊ C2×#689

Subgroups

subgroupG/H
centerC22#1201
commutator, cosocleC3×C4×C5C23
FrattiniC4C2×D3×D5
FittingC2×C3×C4×C5C22
socle, prime radicalC22×C3×C5D4
hypercenterC2×C4D3×D5
hypocenterC3×C5C2×Q16
LCSG ▷ C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 26 points:

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

Conjugacy classes & character table

60 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11747040, #11747061, #11747069, …
maximal normal subgroup of#11747040, #11747061, #11747069, …
maximal quotient of#11746923, #11746924, #11746954, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 394);