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C13×D1155 #44473255

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

Aliases

direct productC13×D1155
unambiguous semidirect productC3⋊(C13×D385)
unambiguous semidirect productC5⋊(C13×D231)
unambiguous semidirect productC7⋊(C13×D165)
unambiguous semidirect productC11⋊(C13×D105)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC3×C5×C7×C11 ⋊ C2×C13
HallC5×C7×C11×C13 ⋊ D3
HallC3×C7×C11×C13 ⋊ D5
HallC3×C5×C11×C13 ⋊ D7
HallC3×C5×C7×C13 ⋊ D11
HallC7×C11×C13 ⋊ D15
HallC5×C11×C13 ⋊ D21
HallC5×C7×C13 ⋊ D33
HallC3×C11×C13 ⋊ D35
HallC5×C7×C11 ⋊ D3×C13
HallC3×C7×C13 ⋊ D55
HallC3×C7×C11 ⋊ D5×C13
HallC3×C5×C13 ⋊ D77
HallC3×C5×C11 ⋊ C13×D7
HallC11×C13 ⋊ D105
HallC3×C5×C7 ⋊ C13×D11
HallC7×C13 ⋊ D165
HallC7×C11 ⋊ C13×D15
HallC5×C13 ⋊ D231
HallC5×C11 ⋊ C13×D21
HallC3×C13 ⋊ D385
HallC5×C7 ⋊ C13×D33
HallC3×C11 ⋊ C13×D35
HallC3×C7 ⋊ C13×D55
HallC3×C5 ⋊ C13×D77
SylowC11 ⋊ C13×D105
SylowC7 ⋊ C13×D165
SylowC5 ⋊ C13×D231
SylowC3 ⋊ C13×D385

Subgroups

subgroupG/H
center, hypercenterC13D1155
commutator, cosocle, hypocenterC3×C5×C7×C11C2×C13
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C13

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

7527 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 40);