Finite Group Databasebeta

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C2×C4×C5×D17 #13062819

order1360
isoclinismisoclinic class of D17
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×C5×D17

Splittings

FittingC2×C4×C5×C17 ⋊ C2
derived, SylowC17 ⋊ C22×C4×C5
HallC5×C17 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4×C5D17
commutator, hypocenterC17C22×C4×C5
FrattiniC2C22×C5×D17
FittingC2×C4×C5×C17C2
socleC22×C5×C17C22
prime radicalC22×C5×D17C2
cosocleC2×C17C23×C5
LCSG ▷ C17
UCSC1 ◁ C2×C4×C5

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 680

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 187);