Finite Group Databasebeta

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Cayley diagram

C2×C5×C4⋊Dic3 #91728

order480
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C5×C4⋊Dic3

Splittings

HallC3×C5 ⋊ C2×C4⋊C4
SylowC3 ⋊ C2×C5×C4⋊C4

Subgroups

subgroupG/H
centerC23×C5C2×D3
commutatorC2×C3C22×C4×C5
FrattiniC22C22×C5×D3
FittingC22×C3×C4×C5C2
socle, prime radicalC23×C3×C5C22
cosocleC22×C3C23×C5
hypercenterC22×C4×C5D3
hypocenterC3C2×C5×C4⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C22×C4×C5

184 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:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745979, #11745981, #11745986, …
maximal normal subgroup of#11745979, #11745981, #11745986, …
maximal quotient ofC2×C5×C4⋊(C3⋊C8), C5×#4924, C4×C5×C4⋊Dic3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 804);