Finite Group Databasebeta

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C7×D65⋊D17 #44525930

order30940
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC7×D65⋊D17
unambiguous semidirect productD65⋊(C7×D17)
unambiguous semidirect productD85⋊(C7×D13)
unambiguous semidirect productD221⋊(C7×D5)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C22
derived, HallC5×C13×C17 ⋊ C22×C7
HallC7×C13×C17 ⋊ C2×D5
HallC5×C7×C17 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×C7×D5
HallC7×C17 ⋊ D5×D13
HallC7×C13 ⋊ D5×D17
HallC5×C17 ⋊ C2×C7×D13
HallC5×C13 ⋊ C2×C7×D17
HallC5×C7 ⋊ D13×D17
SylowC17 ⋊ C7×D5×D13
SylowC13 ⋊ C7×D5×D17
SylowC5 ⋊ C7×D13×D17

Subgroups

subgroupG/H
center, hypercenterC7D65⋊D17
commutator, cosocle, hypocenterC5×C13×C17C22×C7
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C5×C13×C17
UCSC1 ◁ C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 80);