Finite Group Databasebeta

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Cayley diagram

C2×C5×#217 #91755

order480
isoclinismisoclinic class of Dic6
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C24

Aliases

direct productC2×C5×#217

Splittings

HallC3×C5 ⋊ C2×C22⋊C4
SylowC3 ⋊ C2×C5×C22⋊C4

Subgroups

subgroupG/H
centerC23×C5C2×D3
commutatorC2×C3C22×C4×C5
FrattiniC22C22×C5×D3
Fitting, prime radicalC24×C3×C5C2
socleC23×C3×C5C22
cosocleC22×C3C23×C5
hypercenterC24×C5D3
hypocenterC3C2×C5×C22⋊C4
LCSG ▷ C2×C3 ▷ C3
UCSC1 ◁ C23×C5 ◁ C24×C5

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 18
transitive degreeμt(G) = 240

A minimal faithful permutation representation — 3 generators on 18 points:

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

Conjugacy classes & character table

180 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11746018, #11746019, #11746020, …
maximal normal subgroup of#11746018, #11746019, #11746020, …
maximal quotient ofC2×C5×#830, C5×#5207, C2×C5×C3⋊#95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 831);