Finite Group Databasebeta

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Cayley diagram

C4×Dic30 #91757

order480
isoclinismisoclinic class of Dic30
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC4×Dic30

Splittings

HallC3×C5 ⋊ C4×Q8
SylowC5 ⋊ C4×Dic6
SylowC3 ⋊ C4×Dic10

Subgroups

subgroupG/H
centerC2×C4C2×D15
commutatorC2×C3×C5C22×C4
FrattiniC22C22×D15
FittingC3×C42×C5C2
socle, prime radical, cosocleC22×C3×C5C23
hypercenterC42D15
hypocenterC3×C5C4×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C42

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 20
transitive degreeμt(G) = 480

A minimal faithful permutation representation — 3 generators on 20 points:

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

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745844, #11745845, #11746277, …
maximal normal subgroup of#11745844, #11745845, #11746277, …
maximal quotient of#11750747, #11750748, #11750755, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 833);