Finite Group Databasebeta

← Prev (#44473253) Next (#44473255) →

C11×D1365 #44473254

order30030
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1365
unambiguous semidirect productC3⋊(C11×D455)
unambiguous semidirect productC5⋊(C11×D273)
unambiguous semidirect productC7⋊(C11×D195)
unambiguous semidirect productC13⋊(C11×D105)

Splittings

Fitting, socle, HallC3×C5×C7×C11×C13 ⋊ C2
derived, HallC3×C5×C7×C13 ⋊ C2×C11
HallC5×C7×C11×C13 ⋊ D3
HallC3×C7×C11×C13 ⋊ D5
HallC3×C5×C11×C13 ⋊ D7
HallC3×C5×C7×C11 ⋊ D13
HallC7×C11×C13 ⋊ D15
HallC5×C11×C13 ⋊ D21
HallC5×C7×C13 ⋊ D3×C11
HallC3×C11×C13 ⋊ D35
HallC5×C7×C11 ⋊ D39
HallC3×C7×C13 ⋊ D5×C11
HallC3×C7×C11 ⋊ D65
HallC3×C5×C13 ⋊ C11×D7
HallC3×C5×C11 ⋊ D91
HallC11×C13 ⋊ D105
HallC3×C5×C7 ⋊ C11×D13
HallC7×C13 ⋊ C11×D15
HallC7×C11 ⋊ D195
HallC5×C13 ⋊ C11×D21
HallC5×C11 ⋊ D273
HallC3×C13 ⋊ C11×D35
HallC5×C7 ⋊ C11×D39
HallC3×C11 ⋊ D455
HallC3×C7 ⋊ C11×D65
HallC3×C5 ⋊ C11×D91
SylowC13 ⋊ C11×D105
SylowC7 ⋊ C11×D195
SylowC5 ⋊ C11×D273
SylowC3 ⋊ C11×D455

Subgroups

subgroupG/H
center, hypercenterC11D1365
commutator, cosocle, hypocenterC3×C5×C7×C13C2×C11
FrattiniC1G
Fitting, socleC3×C5×C7×C11×C13C2
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C11

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15015

Conjugacy classes & character table

7524 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30030, 39);