Finite Group Databasebeta

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C3×C7×C13×D55 #44473235

order30030
automorphism?
homologyAbelianization (H1) = C2×C3×C7×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×C13×D55
unambiguous semidirect productC5⋊(C3×C7×C13×D11)
unambiguous semidirect productC11⋊(C3×C7×D5×C13)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC5×C11 ⋊ C2×C3×C7×C13
HallC5×C7×C11×C13 ⋊ C2×C3
HallC3×C7×C11×C13 ⋊ D5
HallC3×C5×C11×C13 ⋊ C2×C7
HallC3×C5×C7×C13 ⋊ D11
HallC3×C5×C7×C11 ⋊ C2×C13
HallC7×C11×C13 ⋊ C3×D5
HallC5×C11×C13 ⋊ C2×C3×C7
HallC5×C7×C13 ⋊ C3×D11
HallC3×C11×C13 ⋊ C7×D5
HallC5×C7×C11 ⋊ C2×C3×C13
HallC3×C7×C11 ⋊ D5×C13
HallC3×C5×C13 ⋊ C7×D11
HallC3×C5×C11 ⋊ C2×C7×C13
HallC11×C13 ⋊ C3×C7×D5
HallC3×C5×C7 ⋊ C13×D11
HallC7×C11 ⋊ C3×D5×C13
HallC5×C13 ⋊ C3×C7×D11
HallC5×C7 ⋊ C3×C13×D11
HallC3×C11 ⋊ C7×D5×C13
HallC3×C5 ⋊ C7×C13×D11
SylowC11 ⋊ C3×C7×D5×C13
SylowC5 ⋊ C3×C7×C13×D11

Subgroups

subgroupG/H
center, hypercenterC3×C7×C13D55
commutator, cosocle, hypocenterC5×C11C2×C3×C7×C13
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C5×C11
UCSC1 ◁ C3×C7×C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

7917 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 20);