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C5×C11×A4×C13 #22575180

order8580
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C5×C11×C13 · Schur multiplier (H2) = C2

Aliases

direct productC5×C11×A4×C13
unambiguous semidirect productC22⋊(C3×C5×C11×C13)
unambiguous semidirect product(C22×C5)⋊(C3×C11×C13)
unambiguous semidirect product(C22×C5×C11)⋊(C3×C13)

Splittings

Fitting, socle, HallC22×C5×C11×C13 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C11×C13
HallC22×C11×C13 ⋊ C3×C5
HallC22×C5×C13 ⋊ C3×C11
HallC22×C5×C11 ⋊ C3×C13
HallC22×C13 ⋊ C3×C5×C11
HallC22×C11 ⋊ C3×C5×C13
HallC22×C5 ⋊ C3×C11×C13

Subgroups

subgroupG/H
center, hypercenterC5×C11×C13A4
commutator, hypocenterC22C3×C5×C11×C13
FrattiniC1G
Fitting, socleC22×C5×C11×C13C3
LCSG ▷ C22
UCSC1 ◁ C5×C11×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2860 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×A4×C13⋊C3, C3×C5×C11×A4×C13
maximal normal subgroup ofC5×C11×A4×C13⋊C3, C3×C5×C11×A4×C13
maximal quotient ofC5×C11×C13×C22⋊C9, C3×C5×C11×A4×C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 152);