Finite Group Databasebeta

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C7×C25×D33 #26040449

order11550
isoclinismisoclinic class of D33
automorphism?
homologyAbelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC7×C25×D33
unambiguous semidirect productC3⋊(C7×D11×C25)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C2
derived, HallC3×C11 ⋊ C2×C7×C25
HallC7×C11×C25 ⋊ D3
HallC3×C11×C25 ⋊ C2×C7
HallC3×C7×C25 ⋊ D11
HallC11×C25 ⋊ D3×C7
HallC3×C7×C11 ⋊ C2×C25
HallC7×C11 ⋊ D3×C25
HallC3×C25 ⋊ C7×D11
HallC3×C7 ⋊ D11×C25
SylowC11 ⋊ D3×C7×C25
SylowC3 ⋊ C7×D11×C25

Subgroups

subgroupG/H
center, hypercenterC7×C25D33
commutator, hypocenterC3×C11C2×C7×C25
FrattiniC5C5×C7×D33
FittingC3×C7×C11×C25C2
socleC3×C5×C7×C11C2×C5
prime radicalC5×C7×D33C5
cosocleC3×C5×C11C2×C5×C7
LCSG ▷ C3×C11
UCSC1 ◁ C7×C25

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofD3×C7×D11×C25, D7×C25×D33, C25×D21⋊D11, …
maximal normal subgroup ofD3×C7×D11×C25, D7×C25×D33, C25×D21⋊D11, …
maximal quotient ofC7×C25×Dic33, C2×C7×C25×D33, C7×C25×D99, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 13);