Finite Group Databasebeta

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Cayley diagram

C2×#6821 #92097

order480
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC2×#6821

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ C2×#41
SylowC5 ⋊ C2×#239
SylowC3 ⋊ C2×#713

Subgroups

subgroupG/H
centerC22C22×D15
commutator, cosocleC2×C3×C5C24
FrattiniC2C23×D15
FittingC2×C3×C5×Q8C2
socleC22×C3×C5C23
hypercenterC2×Q8D15
hypocenterC3×C5C2×#41
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

328 conjugacy classes of subgroups.

Full subgroup data →

Presentation

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

A minimal faithful permutation representation — 4 generators on 18 points:

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

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749205, #11749215, #11749288, …
maximal normal subgroup of#11749205, #11749215, #11749288, …
maximal quotient ofC2×#91779, C2×#91781, C2×#91782, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1173);