Finite Group Databasebeta

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C5×C7×A4×C29 #27131813

order12180
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C3×C5×C7×C29 · Schur multiplier (H2) = C2

Aliases

direct productC5×C7×A4×C29
unambiguous semidirect productC22⋊(C3×C5×C7×C29)
unambiguous semidirect product(C22×C5)⋊(C3×C7×C29)

Splittings

Fitting, socle, HallC22×C5×C7×C29 ⋊ C3
derived, SylowC22 ⋊ C3×C5×C7×C29
HallC22×C7×C29 ⋊ C3×C5
HallC22×C5×C29 ⋊ C3×C7
HallC22×C5×C7 ⋊ C3×C29
HallC22×C29 ⋊ C3×C5×C7
HallC22×C7 ⋊ C3×C5×C29
HallC22×C5 ⋊ C3×C7×C29

Subgroups

subgroupG/H
center, hypercenterC5×C7×C29A4
commutator, hypocenterC22C3×C5×C7×C29
FrattiniC1G
Fitting, socleC22×C5×C7×C29C3
LCSG ▷ C22
UCSC1 ◁ C5×C7×C29

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4060 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×A4×ΓL(1,𝔽8)×C29, C3×C5×C7×A4×C29
maximal normal subgroup ofC5×A4×ΓL(1,𝔽8)×C29, C3×C5×C7×A4×C29
maximal quotient ofC5×C7×C29×C22⋊C9, C3×C5×C7×A4×C29

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12180, 148);