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C3×D1925 #26040447

order11550
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC3×D1925
unambiguous semidirect productC11⋊(C3×D175)
unambiguous semidirect productC25⋊(C3×D77)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C2
derived, HallC7×C11×C25 ⋊ C2×C3
HallC3×C11×C25 ⋊ D7
HallC3×C7×C25 ⋊ D11
HallC11×C25 ⋊ C3×D7
HallC3×C7×C11 ⋊ D25
HallC7×C25 ⋊ C3×D11
HallC7×C11 ⋊ C3×D25
HallC3×C25 ⋊ D77
HallC3×C11 ⋊ D175
SylowC25 ⋊ C3×D77
HallC3×C7 ⋊ D275
SylowC11 ⋊ C3×D175
SylowC7 ⋊ C3×D275

Subgroups

subgroupG/H
center, hypercenterC3D1925
commutator, cosocle, hypocenterC7×C11×C25C2×C3
FrattiniC5C3×D385
FittingC3×C7×C11×C25C2
socleC3×C5×C7×C11D5
LCSG ▷ C7×C11×C25
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2892 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×D11×D175, C3×D7×D275, C3×D25×D77, …
maximal normal subgroup ofC3×D11×D175, C3×D7×D275, C3×D25×D77, …
maximal quotient ofC3×Dic1925, C2×C3×D1925, C9×D1925, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 11);