Finite Group Databasebeta

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C2×C7×C13×D85 #44525967

order30940
automorphism?
homologyAbelianization (H1) = C22×C7×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×C13×D85
unambiguous semidirect product(C2×C5)⋊(C7×C13×D17)
unambiguous semidirect product(C2×C17)⋊(C7×D5×C13)

Splittings

Fitting, socleC2×C5×C7×C13×C17 ⋊ C2
derived, HallC5×C17 ⋊ C22×C7×C13
HallC5×C7×C13×C17 ⋊ C22
HallC7×C13×C17 ⋊ C2×D5
HallC5×C13×C17 ⋊ C22×C7
HallC5×C7×C17 ⋊ C22×C13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×C7×D5
HallC7×C17 ⋊ C2×D5×C13
HallC5×C13 ⋊ C2×C7×D17
HallC5×C7 ⋊ C2×C13×D17
SylowC17 ⋊ C2×C7×D5×C13
SylowC5 ⋊ C2×C7×C13×D17

Subgroups

subgroupG/H
center, hypercenterC2×C7×C13D85
commutator, cosocle, hypocenterC5×C17C22×C7×C13
FrattiniC1G
Fitting, socleC2×C5×C7×C13×C17C2
LCSG ▷ C5×C17
UCSC1 ◁ C2×C7×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15470

Conjugacy classes & character table

8008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 117);