Finite Group Databasebeta

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C2×C4×D5×C17 #13062829

order1360
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23

Aliases

direct productC2×C4×D5×C17

Splittings

FittingC2×C4×C5×C17 ⋊ C2
derived, SylowC5 ⋊ C22×C4×C17
HallC5×C17 ⋊ C22×C4

Subgroups

subgroupG/H
center, hypercenterC2×C4×C17D5
commutator, hypocenterC5C22×C4×C17
FrattiniC2C22×D5×C17
FittingC2×C4×C5×C17C2
socleC22×C5×C17C22
prime radicalC22×D5×C17C2
cosocleC2×C5C23×C17
LCSG ▷ C5
UCSC1 ◁ C2×C4×C17

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 680

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1360, 197);