Finite Group Databasebeta

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C11×(C61⋊C5)⋊C9 #44474918

order30195
automorphism?
homologyAbelianization (H1) = C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×(C61⋊C5)⋊C9
unambiguous semidirect product(C61⋊C5)⋊(C9×C11)
unambiguous semidirect product(C61⋊C9)⋊(C5×C11)
unambiguous semidirect product(C11×C61⋊C5)⋊C9

Splittings

derived, SylowC61 ⋊ C5×C9×C11
HallC11×C61⋊C9 ⋊ C5
HallC11×C61⋊C5 ⋊ C9
HallC11×C61 ⋊ C5×C9
HallC61⋊C9 ⋊ C5×C11
HallC61⋊C5 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C11(C61⋊C3)⋊C5
commutator, hypocenterC61C5×C9×C11
FrattiniC3C11×(C61⋊C3)⋊C5
Fitting, socleC3×C11×C61C3×C5
prime radicalC3×C11×C61⋊C5C3
cosocleC3×C61C3×C5×C11
LCSG ▷ C61
UCSC1 ◁ C3×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6039

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30195, 9);