Finite Group Databasebeta

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C3×D25×C29⋊C7 #44478536

order30450
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×D25×C29⋊C7
unambiguous semidirect productC25⋊(C2×C3×C29⋊C7)
unambiguous semidirect product(C29×D25)⋊(C3×C7)
unambiguous semidirect product(C3×C29×D25)⋊C7

Splittings

Fitting, HallC3×C25×C29 ⋊ C2×C7
derived, HallC25×C29 ⋊ C2×C3×C7
HallC3×C25×C29⋊C7 ⋊ C2
HallC25×C29⋊C7 ⋊ C2×C3
HallC3×C29×D25 ⋊ C7
HallC29×D25 ⋊ C3×C7
HallC3×C29 ⋊ C7×D25
HallC3×C25 ⋊ C2×C29⋊C7
SylowC29 ⋊ C3×C7×D25
SylowC25 ⋊ C2×C3×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC3D25×C29⋊C7
commutator, cosocle, hypocenterC25×C29C2×C3×C7
FrattiniC5C3×D5×C29⋊C7
FittingC3×C25×C29C2×C7
socleC3×C5×C29C7×D5
LCSG ▷ C25×C29
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2175

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 20);