Finite Group Databasebeta

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A4×C29×C52⋊C3 #39908065

order26100
automorphism?
homologyAbelianization (H1) = C32×C29 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productA4×C29×C52⋊C3
unambiguous semidirect product(C22×C52⋊C3)⋊(C3×C29)
unambiguous semidirect product(C52×A4)⋊(C3×C29)
unambiguous semidirect product(C22⋊(C52⋊C3))⋊(C3×C29)
unambiguous semidirect product(C29×C22⋊(C52⋊C3))⋊C3
unambiguous semidirect product(C52×A4×C29)⋊C3
unambiguous semidirect product(C22×C29×C52⋊C3)⋊C3

Splittings

Fitting, socle, HallC22×C52×C29 ⋊ C32
derived, HallC22×C52 ⋊ C32×C29
HallC52×C29 ⋊ C3×A4
HallC22×C29 ⋊ C3×C52⋊C3
SylowC52 ⋊ C3×A4×C29
SylowC22 ⋊ C3×C29×C52⋊C3

Subgroups

subgroupG/H
center, hypercenterC29A4×C52⋊C3
commutator, cosocle, hypocenterC22×C52C32×C29
FrattiniC1G
Fitting, socleC22×C52×C29C32
LCSG ▷ C22×C52
UCSC1 ◁ C29

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1740

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 299);