Finite Group Databasebeta

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C5×C11⋊(D31⋊C9) #44501707

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊(D31⋊C9)
unambiguous semidirect product(C5×D341)⋊C9

Splittings

derived, HallC11×C31 ⋊ C2×C5×C9
HallC5×C11×C31⋊C9 ⋊ C2
HallC5×D341 ⋊ C9
HallC11×C31⋊C9 ⋊ C2×C5
HallC5×C11×C31 ⋊ C2×C9
HallC5×C31⋊C9 ⋊ D11
HallD341 ⋊ C5×C9
HallC31⋊C9 ⋊ C5×D11
HallC5×C31 ⋊ C9×D11
HallC5×C11 ⋊ D31⋊C9
SylowC31 ⋊ C5×C9×D11
SylowC11 ⋊ C5×D31⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C11⋊(D31⋊C3)
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C5×C11⋊(D31⋊C3)
Fitting, socleC3×C5×C11×C31C2×C3
prime radicalC3×C5×D341C3
cosocleC3×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

1140 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 74);