Finite Group Databasebeta

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C2×C5×Dic34 #13062818

order1360
isoclinismisoclinic class of Dic34
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C22

Aliases

direct productC2×C5×Dic34
unambiguous semidirect product(C2×C17)⋊(C5×Q8)

Splittings

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

Subgroups

subgroupG/H
centerC22×C5C2×D17
commutator, cosocleC2×C17C23×C5
FrattiniC2C22×C5×D17
FittingC2×C4×C5×C17C2
socle, prime radicalC22×C5×C17C22
hypercenterC2×C4×C5D17
hypocenterC17C2×C5×Q8
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C22×C5 ◁ C2×C4×C5

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1360

Conjugacy classes & character table

370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 186);