Finite Group Databasebeta

← Prev (#44478937) Next (#44478939) →

C2×C7×(C11⋊D11)⋊C9 #44478938

order30492
automorphism?
homologyAbelianization (H1) = C22×C7×C9 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×C7×(C11⋊D11)⋊C9
unambiguous semidirect product(C2×C11⋊D11)⋊(C7×C9)

Splittings

derived, SylowC112 ⋊ C22×C7×C9
HallC7×C112⋊C9 ⋊ C22
HallC2×C7×C11⋊D11 ⋊ C9
HallC112⋊C9 ⋊ C22×C7
HallC7×C112 ⋊ C22×C9
HallC2×C11⋊D11 ⋊ C7×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7(C11⋊D11)⋊C3
commutator, hypocenterC112C22×C7×C9
FrattiniC3C2×C7×(C11⋊D11)⋊C3
Fitting, socleC2×C3×C7×C112C2×C3
prime radicalC2×C3×C7×C11⋊D11C3
cosocleC3×C112C22×C3×C7
LCSG ▷ C112
UCSC1 ◁ C2×C3×C7

140 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1386

Conjugacy classes & character table

1092 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 161);