Finite Group Databasebeta

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Cayley diagram

C2×Q8×D15 #92096

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

Aliases

direct productC2×Q8×D15

Splittings

FittingC2×C3×C5×Q8 ⋊ C2
HallC3×C5 ⋊ C22×Q8
SylowC5 ⋊ C2×D3×Q8
SylowC3 ⋊ C2×Q8×D5

Subgroups

subgroupG/H
centerC22C22×D15
commutator, cosocleC2×C3×C5C24
FrattiniC2C23×D15
FittingC2×C3×C5×Q8C2
socleC22×C3×C5C23
prime radicalC22×D15C22
hypercenterC2×Q8D15
hypocenterC3×C5C22×Q8
LCSG ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C2×Q8

312 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)(4,5)(7,8)(9,10);(3,4,5)(6,7,9,10,8)(11,13,14,18)(12,15,16,17);(11,12,14,16)(13,17,18,15);(1,2)

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#11749203, #11749218, #11749286, …
maximal normal subgroup of#11749203, #11749218, #11749286, …
maximal quotient ofC2×#91776, C2×#91777, C2×#91778, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(480, 1172);