Finite Group Databasebeta

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C11×D1395 #44501660

order30690
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1395
unambiguous semidirect productC5⋊(C11×D279)
unambiguous semidirect productC9⋊(C11×D155)
unambiguous semidirect productC31⋊(C11×D45)

Splittings

Fitting, HallC5×C9×C11×C31 ⋊ C2
derived, HallC5×C9×C31 ⋊ C2×C11
HallC9×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ D9
HallC5×C9×C11 ⋊ D31
HallC11×C31 ⋊ D45
HallC9×C31 ⋊ D5×C11
HallC5×C31 ⋊ C11×D9
HallC9×C11 ⋊ D155
HallC5×C11 ⋊ D279
HallC5×C9 ⋊ C11×D31
SylowC31 ⋊ C11×D45
SylowC9 ⋊ C11×D155
SylowC5 ⋊ C11×D279

Subgroups

subgroupG/H
center, hypercenterC11D1395
commutator, cosocle, hypocenterC5×C9×C31C2×C11
FrattiniC3C11×D465
FittingC5×C9×C11×C31C2
socleC3×C5×C11×C31D3
LCSG ▷ C5×C9×C31
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

7689 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 27);