Finite Group Databasebeta

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C2×C17×D71⋊C7 #46798796

order33796
automorphism?
homologyAbelianization (H1) = C22×C7×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D71⋊C7
unambiguous semidirect productD71⋊(C2×C7×C17)
unambiguous semidirect product(C2×D71)⋊(C7×C17)
unambiguous semidirect product(C71⋊C7)⋊(C22×C17)
unambiguous semidirect product(C2×C71⋊C7)⋊(C2×C17)
unambiguous semidirect product(C2×C17×D71)⋊C7

Splittings

Fitting, socleC2×C17×C71 ⋊ C2×C7
derived, SylowC71 ⋊ C22×C7×C17
HallC17×C71⋊C7 ⋊ C22
HallC2×C17×D71 ⋊ C7
HallC17×C71 ⋊ C22×C7
HallC71⋊C7 ⋊ C22×C17
HallC2×D71 ⋊ C7×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D71⋊C7
commutator, cosocle, hypocenterC71C22×C7×C17
FrattiniC1G
Fitting, socleC2×C17×C71C2×C7
LCSG ▷ C71
UCSC1 ◁ C2×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2414

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33796, 17);