Finite Group Databasebeta

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D5×C13×D7×C17 #44525943

order30940
automorphism?
homologyAbelianization (H1) = C22×C13×C17 · Schur multiplier (H2) = C2

Aliases

direct productD5×C13×D7×C17
unambiguous semidirect product(C7×D5)⋊(C2×C13×C17)
unambiguous semidirect product(C5×D7)⋊(C2×C13×C17)
unambiguous semidirect productD35⋊(C2×C13×C17)

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC13×C17D5×D7
commutator, cosocle, hypocenterC5×C7C22×C13×C17
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C5×C7
UCSC1 ◁ C13×C17

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

4420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 93);