Finite Group Databasebeta

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C52×C3⋊(D29⋊C7) #44478561

order30450
automorphism?
homologyAbelianization (H1) = C2×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC52×C3⋊(D29⋊C7)
unambiguous semidirect productC3⋊(C52×D29⋊C7)
unambiguous semidirect productD87⋊(C52×C7)
unambiguous semidirect product(C29⋊C7)⋊(C52×D3)
unambiguous semidirect product(C5×D87)⋊(C5×C7)
unambiguous semidirect product(C52×D87)⋊C7

Splittings

Fitting, socle, HallC3×C52×C29 ⋊ C2×C7
derived, HallC3×C29 ⋊ C2×C52×C7
HallC3×C52×C29⋊C7 ⋊ C2
HallC52×C29⋊C7 ⋊ D3
HallC52×D87 ⋊ C7
HallC52×C29 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ C2×C52
HallC29⋊C7 ⋊ C52×D3
HallD87 ⋊ C52×C7
HallC3×C52 ⋊ D29⋊C7
SylowC29 ⋊ C52×D3×C7
SylowC3 ⋊ C52×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC52C3⋊(D29⋊C7)
commutator, cosocle, hypocenterC3×C29C2×C52×C7
FrattiniC1G
Fitting, socleC3×C52×C29C2×C7
LCSG ▷ C3×C29
UCSC1 ◁ C52

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2175

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 45);