Finite Group Databasebeta

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C5×C13×D7×D17 #44525876

order30940
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC5×C13×D7×D17
unambiguous semidirect product(D7×C17)⋊(C2×C5×C13)
unambiguous semidirect product(C7×D17)⋊(C2×C5×C13)
unambiguous semidirect productD119⋊(C2×C5×C13)

Splittings

Fitting, socle, HallC5×C7×C13×C17 ⋊ C22
derived, HallC7×C17 ⋊ C22×C5×C13
HallC7×C13×C17 ⋊ C22×C5
HallC5×C13×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C22×C13
HallC5×C7×C13 ⋊ C2×D17
HallC13×C17 ⋊ C2×C5×D7
HallC7×C13 ⋊ C2×C5×D17
HallC5×C17 ⋊ C2×C13×D7
HallC5×C7 ⋊ C2×C13×D17
SylowC17 ⋊ C2×C5×C13×D7
SylowC7 ⋊ C2×C5×C13×D17

Subgroups

subgroupG/H
center, hypercenterC5×C13D7×D17
commutator, cosocle, hypocenterC7×C17C22×C5×C13
FrattiniC1G
Fitting, socleC5×C7×C13×C17C22
LCSG ▷ C7×C17
UCSC1 ◁ C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7735

Conjugacy classes & character table

3250 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30940, 26);