Finite Group Databasebeta

← Prev (#91638) Next (#91640) →

Cayley diagram

C2×C3×C4×Dic5 #91639

order480
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C3×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct productC2×C3×C4×Dic5

Splittings

derived, SylowC5 ⋊ C2×C3×C42
HallC3×C5 ⋊ C2×C42

Subgroups

subgroupG/H
center, hypercenterC22×C3×C4D5
commutator, hypocenterC5C2×C3×C42
FrattiniC22C22×C3×D5
FittingC22×C3×C4×C5C2
socle, prime radicalC23×C3×C5C22
cosocleC22×C5C23×C3
LCSG ▷ C5
UCSC1 ◁ C22×C3×C4

216 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 18 points:

(1,2)(3,4,5)(6,7,8,9)(15,16)(17,18);(10,11,12,13)(14,15,17,18,16);(1,2)

Conjugacy classes & character table

192 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745966, #11745977, #11745978, …
maximal normal subgroup of#11745966, #11745977, #11745978, …
maximal quotient ofC2×C3×C4×#168, C2×C3×#3935, C3×C4×#681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 715);