Finite Group Databasebeta

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Cayley diagram

C22×C5×#67 #92088

order480
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C26

Aliases

direct productC22×C5×#67

Splittings

FittingC24×C3×C5 ⋊ C2
HallC3×C5 ⋊ C22×D4
SylowC3 ⋊ C22×C5×D4

Subgroups

subgroupG/H
centerC23×C5C2×D3
commutator, cosocleC2×C3C24×C5
FrattiniC2C23×C5×D3
FittingC24×C3×C5C2
socleC23×C3×C5C22
hypercenterC24×C5D3
hypocenterC3C22×C5×D4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C24×C5

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 16
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 4 generators on 16 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#90996, #11749482, #11749492, …
maximal normal subgroup ofC2×#90996, #11749482, #11749492, …
maximal quotient ofC22×C5×Dic3⋊C4, C2×C5×#924, C22×C5×(C2×D3)⋊C4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1164);