Finite Group Databasebeta

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C5×C7×D13×D17 #44525874

order30940
automorphism?
homologyAbelianization (H1) = C22×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×D13×D17
unambiguous semidirect product(C17×D13)⋊(C2×C5×C7)
unambiguous semidirect product(C13×D17)⋊(C2×C5×C7)
unambiguous semidirect productD221⋊(C2×C5×C7)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC5×C7D13×D17
commutator, cosocle, hypocenterC13×C17C22×C5×C7
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C13×C17
UCSC1 ◁ C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 24);