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C3×C7⋊(D11⋊C25) #26040458

order11550
automorphism?
homologyAbelianization (H1) = C2×C3×C25 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(D11⋊C25)
unambiguous semidirect product(C11⋊C25)⋊(C3×D7)
unambiguous semidirect product(C3×D77)⋊C25

Splittings

derived, HallC7×C11 ⋊ C2×C3×C25
HallC3×C7×C11⋊C25 ⋊ C2
HallC7×C11⋊C25 ⋊ C2×C3
HallC3×C11⋊C25 ⋊ D7
HallC3×D77 ⋊ C25
HallC11⋊C25 ⋊ C3×D7
HallC3×C7×C11 ⋊ C2×C25
HallD77 ⋊ C3×C25
HallC3×C11 ⋊ D7×C25
HallC3×C7 ⋊ D11⋊C25
SylowC11 ⋊ C3×D7×C25
SylowC7 ⋊ C3×D11⋊C25

Subgroups

subgroupG/H
center, hypercenterC3×C5C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C2×C3×C25
FrattiniC5C3×C7⋊AGL(1,𝔽11)
Fitting, socleC3×C5×C7×C11C2×C5
prime radicalC3×C5×D77C5
cosocleC5×C7×C11C2×C3×C5
LCSG ▷ C7×C11
UCSC1 ◁ C3×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

480 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D7×D11⋊C25, D3×C7⋊(D11⋊C25), D21⋊(D11⋊C25), …
maximal normal subgroup ofC3×D7×D11⋊C25, D3×C7⋊(D11⋊C25), D21⋊(D11⋊C25), …
maximal quotient ofC3×C7⋊(Dic11⋊C25), C2×C3×C7⋊(D11⋊C25), C9×C7⋊(D11⋊C25), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11550, 22);