Finite Group Databasebeta

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C7×C13⋊C3×D55 #44473308

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13⋊C3×D55
unambiguous semidirect productC5⋊(C7×D11×C13⋊C3)
unambiguous semidirect productC11⋊(C7×D5×C13⋊C3)
unambiguous semidirect product(C13×D55)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C11×C13 ⋊ C2×C3
derived, HallC5×C11×C13 ⋊ C2×C3×C7
HallC5×C7×C11×C13⋊C3 ⋊ C2
HallC7×C13×D55 ⋊ C3
HallC7×C11×C13⋊C3 ⋊ D5
HallC5×C11×C13⋊C3 ⋊ C2×C7
HallC13×D55 ⋊ C3×C7
HallC5×C7×C13⋊C3 ⋊ D11
HallC7×C11×C13 ⋊ C3×D5
HallC5×C7×C13 ⋊ C3×D11
HallC11×C13⋊C3 ⋊ C7×D5
HallC5×C7×C11 ⋊ C2×C13⋊C3
HallC5×C13⋊C3 ⋊ C7×D11
HallC11×C13 ⋊ C3×C7×D5
HallC7×C13 ⋊ C3×D55
HallC7×C11 ⋊ D5×C13⋊C3
HallC5×C13 ⋊ C3×C7×D11
HallC5×C11 ⋊ C2×C7×C13⋊C3
HallC5×C7 ⋊ D11×C13⋊C3
SylowC13 ⋊ C3×C7×D55
SylowC11 ⋊ C7×D5×C13⋊C3
SylowC5 ⋊ C7×D11×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C13⋊C3×D55
commutator, cosocle, hypocenterC5×C11×C13C2×C3×C7
FrattiniC1G
Fitting, socleC5×C7×C11×C13C2×C3
LCSG ▷ C5×C11×C13
UCSC1 ◁ C7

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5005

Conjugacy classes & character table

1421 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 93);