Finite Group Databasebeta

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C5×Q8×D17 #13062824

order1360
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC5×Q8×D17

Splittings

FittingC5×Q8×C17 ⋊ C2
HallC5×C17 ⋊ C2×Q8
SylowC17 ⋊ C2×C5×Q8

Subgroups

subgroupG/H
centerC2×C5C22×D17
commutator, cosocleC2×C17C23×C5
FrattiniC2C22×C5×D17
FittingC5×Q8×C17C2
socleC2×C5×C17C23
prime radicalC2×C5×D17C22
hypercenterC5×Q8D17
hypocenterC17C2×C5×Q8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C5 ◁ C5×Q8

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 680

Conjugacy classes & character table

250 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 192);