Finite Group Databasebeta

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C5×C11×D31⋊C9 #44501705

order30690
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derived, SylowC31 ⋊ C2×C5×C9×C11
HallC5×C11×C31⋊C9 ⋊ C2
HallC5×C11×D31 ⋊ C9
HallC11×C31⋊C9 ⋊ C2×C5
HallC5×C11×C31 ⋊ C2×C9
HallC5×C31⋊C9 ⋊ C2×C11
HallC11×D31 ⋊ C5×C9
HallC11×C31 ⋊ C2×C5×C9
HallC5×D31 ⋊ C9×C11
HallC31⋊C9 ⋊ C2×C5×C11
HallC5×C31 ⋊ C2×C9×C11
HallD31 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11D31⋊C3
commutator, hypocenterC31C2×C5×C9×C11
FrattiniC3C5×C11×D31⋊C3
Fitting, socleC3×C5×C11×C31C2×C3
prime radicalC3×C5×C11×D31C3
cosocleC3×C31C2×C3×C5×C11
LCSG ▷ C31
UCSC1 ◁ C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 72);