Finite Group Databasebeta

← Prev (#26040449) Next (#26040451) →

C11×C25×D21 #26040450

order11550
isoclinismisoclinic class of D21
automorphism?
homologyAbelianization (H1) = C2×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×D21
unambiguous semidirect productC3⋊(C11×D7×C25)
unambiguous semidirect productC7⋊(D3×C11×C25)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C2
derived, HallC3×C7 ⋊ C2×C11×C25
HallC7×C11×C25 ⋊ D3
HallC3×C11×C25 ⋊ D7
HallC3×C7×C25 ⋊ C2×C11
HallC3×C7×C11 ⋊ C2×C25
HallC7×C25 ⋊ D3×C11
HallC7×C11 ⋊ D3×C25
HallC3×C25 ⋊ C11×D7
HallC3×C11 ⋊ D7×C25
SylowC7 ⋊ D3×C11×C25
SylowC3 ⋊ C11×D7×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25D21
commutator, hypocenterC3×C7C2×C11×C25
FrattiniC5C5×C11×D21
FittingC3×C7×C11×C25C2
socleC3×C5×C7×C11C2×C5
prime radicalC5×C11×D21C5
cosocleC3×C5×C7C2×C5×C11
LCSG ▷ C3×C7
UCSC1 ◁ C11×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3300 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD11×C25×D21, D3×C11×D7×C25, C25×D21⋊D11, …
maximal normal subgroup ofD11×C25×D21, D3×C11×D7×C25, C25×D21⋊D11, …
maximal quotient ofC11×C25×Dic21, C2×C11×C25×D21, C11×C25×D63, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 14);