Finite Group Databasebeta

C2×C17×Dic10 #13062828

order1360
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C23×C17 · Schur multiplier (H2) = C22

Aliases

direct productC2×C17×Dic10
unambiguous semidirect product(C2×C5)⋊(Q8×C17)

Splittings

HallC5×C17 ⋊ C2×Q8
SylowC5 ⋊ C2×Q8×C17

Subgroups

subgroupG/H
centerC22×C17C2×D5
commutator, cosocleC2×C5C23×C17
FrattiniC2C22×D5×C17
FittingC2×C4×C5×C17C2
socle, prime radicalC22×C5×C17C22
hypercenterC2×C4×C17D5
hypocenterC5C2×Q8×C17
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C17 ◁ C2×C4×C17

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1360

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 196);