Finite Group Databasebeta

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C3×C5×A4×C29 #19104891

order5220
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C5×C29 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3×C5×A4×C29
unambiguous semidirect productC22⋊(C32×C5×C29)
unambiguous semidirect product(C22×C3)⋊(C3×C5×C29)
unambiguous semidirect product(C22×C5)⋊(C32×C29)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C29)
unambiguous semidirect product(C22×C29)⋊(C32×C5)
unambiguous semidirect product(C22×C3×C29)⋊(C3×C5)
unambiguous semidirect product(C22×C5×C29)⋊C32
unambiguous semidirect product(C22×C3×C5×C29)⋊C3

Splittings

Fitting, socleC22×C3×C5×C29 ⋊ C3
derived, SylowC22 ⋊ C32×C5×C29
HallC22×C5×C29 ⋊ C32
HallC22×C29 ⋊ C32×C5
HallC22×C5 ⋊ C32×C29

Subgroups

subgroupG/H
center, hypercenterC3×C5×C29A4
commutator, hypocenterC22C32×C5×C29
FrattiniC1G
Fitting, socleC22×C3×C5×C29C3
LCSG ▷ C22
UCSC1 ◁ C3×C5×C29

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×A4×C25×C29, C3×C52×A4×C29, C3×C5×C29×A5, …
maximal normal subgroup ofC3×A4×C25×C29, C3×C52×A4×C29, C3×C5×A4×C29⋊C7, …
maximal quotient ofC3×A4×C25×C29, C3×C52×A4×C29, C5×A4×ΓL(1,𝔽8)×C29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5220, 101);