Finite Group Databasebeta

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C11×C31×D45 #44501659

order30690
automorphism?
homologyAbelianization (H1) = C2×C11×C31 · Schur multiplier (H2) = C1

Aliases

direct productC11×C31×D45
unambiguous semidirect productC5⋊(C11×D9×C31)
unambiguous semidirect productC9⋊(D5×C11×C31)

Splittings

Fitting, HallC5×C9×C11×C31 ⋊ C2
derived, HallC5×C9 ⋊ C2×C11×C31
HallC9×C11×C31 ⋊ D5
HallC5×C11×C31 ⋊ D9
HallC5×C9×C31 ⋊ C2×C11
HallC5×C9×C11 ⋊ C2×C31
HallC9×C31 ⋊ D5×C11
HallC5×C31 ⋊ C11×D9
HallC9×C11 ⋊ D5×C31
HallC5×C11 ⋊ D9×C31
SylowC9 ⋊ D5×C11×C31
SylowC5 ⋊ C11×D9×C31

Subgroups

subgroupG/H
center, hypercenterC11×C31D45
commutator, cosocle, hypocenterC5×C9C2×C11×C31
FrattiniC3C11×D15×C31
FittingC5×C9×C11×C31C2
socleC3×C5×C11×C31D3
LCSG ▷ C5×C9
UCSC1 ◁ C11×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15345

Conjugacy classes & character table

8184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 26);