Finite Group Databasebeta

C25×C3⋊(D29⋊C7) #44478539

order30450
automorphism?
homologyAbelianization (H1) = C2×C7×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×C3⋊(D29⋊C7)
unambiguous semidirect productC3⋊(C25×D29⋊C7)
unambiguous semidirect productD87⋊(C7×C25)
unambiguous semidirect product(C29⋊C7)⋊(D3×C25)
unambiguous semidirect product(C25×D87)⋊C7

Splittings

Fitting, HallC3×C25×C29 ⋊ C2×C7
derived, HallC3×C29 ⋊ C2×C7×C25
HallC3×C25×C29⋊C7 ⋊ C2
HallC25×C29⋊C7 ⋊ D3
HallC25×D87 ⋊ C7
HallC25×C29 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ C2×C25
HallC29⋊C7 ⋊ D3×C25
HallD87 ⋊ C7×C25
HallC3×C25 ⋊ D29⋊C7
SylowC29 ⋊ D3×C7×C25
SylowC3 ⋊ C25×D29⋊C7

Subgroups

subgroupG/H
center, hypercenterC25C3⋊(D29⋊C7)
commutator, hypocenterC3×C29C2×C7×C25
FrattiniC5C5×C3⋊(D29⋊C7)
FittingC3×C25×C29C2×C7
socle, cosocleC3×C5×C29C2×C5×C7
prime radicalC5×C3⋊(D29⋊C7)C5
LCSG ▷ C3×C29
UCSC1 ◁ C25

48 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, 23);