Finite Group Databasebeta

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C7×D5×C17×D13 #44525927

order30940
automorphism?
homologyAbelianization (H1) = C22×C7×C17 · Schur multiplier (H2) = C2

Aliases

direct productC7×D5×C17×D13
unambiguous semidirect product(D5×C13)⋊(C2×C7×C17)
unambiguous semidirect product(C5×D13)⋊(C2×C7×C17)
unambiguous semidirect productD65⋊(C2×C7×C17)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7×C17D5×D13
commutator, cosocle, hypocenterC5×C13C22×C7×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C5×C13
UCSC1 ◁ C7×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

3808 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 77);