Finite Group Databasebeta

← Prev (#44526241) Next (#44526243) →

C11×D1407 #44526242

order30954
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×D1407
unambiguous semidirect productC3⋊(C11×D469)
unambiguous semidirect productC7⋊(C11×D201)

Splittings

Fitting, socle, HallC3×C7×C11×C67 ⋊ C2
derived, HallC3×C7×C67 ⋊ C2×C11
HallC7×C11×C67 ⋊ D3
HallC3×C11×C67 ⋊ D7
HallC11×C67 ⋊ D21
HallC7×C67 ⋊ D3×C11
HallC3×C7×C11 ⋊ D67
HallC3×C67 ⋊ C11×D7
HallC7×C11 ⋊ D201
SylowC67 ⋊ C11×D21
HallC3×C11 ⋊ D469
HallC3×C7 ⋊ C11×D67
SylowC7 ⋊ C11×D201
SylowC3 ⋊ C11×D469

Subgroups

subgroupG/H
center, hypercenterC11D1407
commutator, cosocle, hypocenterC3×C7×C67C2×C11
FrattiniC1G
Fitting, socleC3×C7×C11×C67C2
LCSG ▷ C3×C7×C67
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15477

Conjugacy classes & character table

7755 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30954, 23);