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C5×A4×C11⋊C5 #15693157

order3300
automorphism?
homologyAbelianization (H1) = C3×C52 · Schur multiplier (H2) = C2×C5

Aliases

direct productC5×A4×C11⋊C5
unambiguous semidirect productC22⋊(C3×C5×C11⋊C5)
unambiguous semidirect productC11⋊(C52×A4)
unambiguous semidirect product(C22×C5)⋊(C3×C11⋊C5)
unambiguous semidirect product(C5×C11)⋊(C5×A4)
unambiguous semidirect product(C11×A4)⋊C52
unambiguous semidirect product(C22×C11⋊C5)⋊(C3×C5)
unambiguous semidirect product(C5×C11×A4)⋊C5
unambiguous semidirect product(C22×C5×C11⋊C5)⋊C3

Splittings

Fitting, socleC22×C5×C11 ⋊ C3×C5
derived, HallC22×C11 ⋊ C3×C52
HallC22×C5×C11⋊C5 ⋊ C3
HallC11×A4 ⋊ C52
SylowC11 ⋊ C52×A4
SylowC22 ⋊ C3×C5×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC5A4×C11⋊C5
commutator, cosocle, hypocenterC22×C11C3×C52
FrattiniC1G
Fitting, socleC22×C5×C11C3×C5
LCSG ▷ C22×C11
UCSC1 ◁ C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

140 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×C7×A4×C11⋊C5, C5×C11⋊C5×C22⋊ΓL(1,𝔽8), C5×A4×C121⋊C5, …
maximal normal subgroup ofC5×C7×A4×C11⋊C5, C5×C11×A4×C11⋊C5, D5×A4×C11⋊C5, …
maximal quotient ofC5×C7×A4×C11⋊C5, C5×C11⋊C5×C22⋊ΓL(1,𝔽8), C5×A4×C121⋊C5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 77);