Finite Group Databasebeta

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Cayley diagram

C2×#6705 #91789

order480
isoclinismisoclinic class of Dic30
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#6705

Splittings

FittingC2×C3×C5×C8 ⋊ C2
HallC3×C5 ⋊ C2×M16
SylowC5 ⋊ C2×ΓL(1,𝔽25)
SylowC3 ⋊ C2×#676

Subgroups

subgroupG/H
centerC2×C4C2×D15
commutatorC2×C3×C5C22×C4
FrattiniC4C22×D15
FittingC2×C3×C5×C8C2
socleC22×C3×C5C2×C4
prime radicalC22×D15C4
cosocleC3×C4×C5C23
hypercenterC2×C8D15
hypocenterC3×C5C2×M16
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C2×C4 ◁ C2×C8

136 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)(6,7,9,10,8)(11,12,13,16,14,15,17,18);(1,2)(4,5)(7,8)(9,10)(12,15)(16,18);(1,2)

Conjugacy classes & character table

132 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11745884, #11746335, #11747592, …
maximal normal subgroup of#11745884, #11746335, #11747592, …
maximal quotient of#11750780, #11750786, C4×#6705, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 865);