Finite Group Databasebeta

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C2×C11⋊C5×C31⋊C9 #44501643

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

Aliases

direct productC2×C11⋊C5×C31⋊C9
unambiguous semidirect product(C2×C11)⋊(C5×C31⋊C9)
unambiguous semidirect product(C2×C31×C11⋊C5)⋊C9

Splittings

derived, HallC11×C31 ⋊ C2×C5×C9
HallC2×C11×C31⋊C9 ⋊ C5
HallC2×C31×C11⋊C5 ⋊ C9
HallC11×C31⋊C9 ⋊ C2×C5
HallC31×C11⋊C5 ⋊ C2×C9
HallC2×C11×C31 ⋊ C5×C9
HallC2×C31 ⋊ C9×C11⋊C5
SylowC31 ⋊ C2×C9×C11⋊C5
HallC2×C11 ⋊ C5×C31⋊C9
SylowC11 ⋊ C2×C5×C31⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3C11⋊C5×C31⋊C3
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C2×C11⋊C5×C31⋊C3
Fitting, socleC2×C3×C11×C31C3×C5
prime radicalC2×C3×C31×C11⋊C5C3
cosocleC3×C11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6138

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 10);