Finite Group Databasebeta

← Prev (#31827558) Next (#31827560) →

C3×C11×D11⋊C25 #31827559

order18150
automorphism?
homologyAbelianization (H1) = C2×C3×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C11×D11⋊C25
unambiguous semidirect productD11⋊(C3×C11×C25)
unambiguous semidirect product(C3×D11)⋊(C11×C25)
unambiguous semidirect product(C11⋊C25)⋊(C2×C3×C11)

Splittings

derivedC11 ⋊ C2×C3×C11×C25
HallC3×C11×C11⋊C25 ⋊ C2
HallC11×C11⋊C25 ⋊ C2×C3
HallC3×C11×D11 ⋊ C25
HallC3×C112 ⋊ C2×C25
HallC11×D11 ⋊ C3×C25
SylowC112 ⋊ C2×C3×C25

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11AGL(1,𝔽11)
commutator, hypocenterC11C2×C3×C11×C25
FrattiniC5C3×C11×AGL(1,𝔽11)
Fitting, socleC3×C5×C112C2×C5
prime radicalC3×C5×C11×D11C5
cosocleC5×C11C2×C3×C5×C11
LCSG ▷ C11
UCSC1 ◁ C3×C5×C11

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1650

Conjugacy classes & character table

1815 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D11×D11⋊C25, D3×C11×D11⋊C25, D33×D11⋊C25, …
maximal normal subgroup ofC3×D11×D11⋊C25, D3×C11×D11⋊C25, D33×D11⋊C25, …
maximal quotient ofC3×C11×Dic11⋊C25, C2×C3×C11×D11⋊C25

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18150, 43);