Finite Group Databasebeta

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Cayley diagram

Dic5×Dic6 #91332

order480
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productDic5×Dic6

Splittings

HallC3×C5 ⋊ C4×Q8
SylowC5 ⋊ C4×Dic6
SylowC3 ⋊ Q8×Dic5

Subgroups

subgroupG/H
center, FrattiniC22C2×D3×D5
commutatorC2×C3×C5C22×C4
FittingC2×C3×C4×C5C22
socle, prime radical, cosocleC22×C3×C5C23
hypercenterC2×C4D3×D5
hypocenterC3×C5C4×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×C4

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:

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

Conjugacy classes & character table

72 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746492, #11746493, #11747261, …
maximal normal subgroup of#11746492, #11746493, #11747261, …
maximal quotient ofDic6×#168, #11746850, #11746863, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 408);