Finite Group Databasebeta

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C13×D17×D35 #44525932

order30940
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×D17×D35
unambiguous semidirect product(C5×D17)⋊(C13×D7)
unambiguous semidirect product(C7×D17)⋊(D5×C13)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C22
derived, HallC5×C7×C17 ⋊ C22×C13
HallC7×C13×C17 ⋊ C2×D5
HallC5×C13×C17 ⋊ C2×D7
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×D5×C13
HallC7×C13 ⋊ D5×D17
HallC5×C17 ⋊ C2×C13×D7
HallC5×C13 ⋊ D7×D17
HallC5×C7 ⋊ C2×C13×D17
SylowC17 ⋊ C2×C13×D35
SylowC7 ⋊ D5×C13×D17
SylowC5 ⋊ C13×D7×D17

Subgroups

subgroupG/H
center, hypercenterC13D17×D35
commutator, cosocle, hypocenterC5×C7×C17C22×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C5×C7×C17
UCSC1 ◁ C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

2470 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 82);