Finite Group Databasebeta

← Prev (#44501645) Next (#44501647) →

C2×#13133722⋊C9 #44501646

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

Aliases

direct productC2×#13133722⋊C9
unambiguous semidirect product(C2×#13133722)⋊C9

Splittings

derived, HallC11×C31 ⋊ C2×C5×C9
HallC2×C11×C31⋊C9 ⋊ C5
HallC2×#13133722 ⋊ C9
HallC11×C31⋊C9 ⋊ C2×C5
Hall#13133722 ⋊ C2×C9
HallC2×C11×C31 ⋊ C5×C9
HallC2×C31⋊C9 ⋊ C11⋊C5
HallC31⋊C9 ⋊ C2×C11⋊C5
HallC2×C31 ⋊ C9×C11⋊C5
SylowC31 ⋊ C2×C9×C11⋊C5
HallC2×C11 ⋊ ΓL(1,𝔽32)⋊C9
SylowC11 ⋊ C2×ΓL(1,𝔽32)⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3#13133722⋊C3
commutator, hypocenterC11×C31C2×C5×C9
FrattiniC3C2×#13133722⋊C3
Fitting, socleC2×C3×C11×C31C3×C5
prime radicalC2×C3×#13133722C3
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

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30690, 13);