Finite Group Databasebeta

← Prev (#44525885) Next (#44525887) →

C5×D91⋊D17 #44525886

order30940
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D91⋊D17
unambiguous semidirect productD91⋊(C5×D17)
unambiguous semidirect productD119⋊(C5×D13)
unambiguous semidirect productD221⋊(C5×D7)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C22
derived, HallC7×C13×C17 ⋊ C22×C5
HallC5×C13×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×C5×D7
HallC7×C17 ⋊ C2×C5×D13
HallC7×C13 ⋊ C2×C5×D17
HallC5×C17 ⋊ D7×D13
HallC5×C13 ⋊ D7×D17
HallC5×C7 ⋊ D13×D17
SylowC17 ⋊ C5×D7×D13
SylowC13 ⋊ C5×D7×D17
SylowC7 ⋊ C5×D13×D17

Subgroups

subgroupG/H
center, hypercenterC5D91⋊D17
commutator, cosocle, hypocenterC7×C13×C17C22×C5
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C7×C13×C17
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 36);