Finite Group Databasebeta

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Cayley diagram

C22×C3×C22⋊D5 #92073

order480
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C24×C3 · Schur multiplier (H2) = C26

Aliases

direct productC22×C3×C22⋊D5

Splittings

FittingC24×C3×C5 ⋊ C2
HallC3×C5 ⋊ C22×D4
SylowC5 ⋊ C22×C3×D4

Subgroups

subgroupG/H
centerC23×C3C2×D5
commutator, cosocleC2×C5C24×C3
FrattiniC2C23×C3×D5
FittingC24×C3×C5C2
socleC23×C3×C5C22
hypercenterC24×C3D5
hypocenterC5C22×C3×D4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C3 ◁ C24×C3

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

Conjugacy classes & character table

156 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×#90995, #11749489, #11749490, …
maximal normal subgroup ofC2×#90995, #11749489, #11749490, …
maximal quotient ofC22×C3×#683, C2×C3×#4070, C22×C3×#685, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1149);