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C5×C11×A4 #10620362

order660
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C5×C11 · Schur multiplier (H2) = C2

Aliases

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

Splittings

Fitting, socle, HallC22×C5×C11 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C11
HallC22×C11 ⋊ C3×C5
HallC22×C5 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11A4
commutator, cosocle, hypocenterC22C3×C5×C11
FrattiniC1G
Fitting, socleC22×C5×C11C3
LCSG ▷ C22
UCSC1 ◁ C5×C11

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 220

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

derived subgroup ofC5⋊(C11⋊S4), C11⋊C5×C5⋊S4
maximal subgroup ofC5×C11×S4, C5×C11⋊S4, C11×C5⋊S4, …
maximal normal subgroup ofC5×C11×S4, C5×C11⋊S4, C11×C5⋊S4, …
maximal quotient ofC5×C11×SL(2,𝔽3), C2×C5×C11×A4, C5×C11×C22⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(660, 32);