Finite Group Databasebeta

D3×C25×C29⋊C7 #44478538

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

Aliases

direct productD3×C25×C29⋊C7
unambiguous semidirect productC3⋊(C2×C25×C29⋊C7)
unambiguous semidirect product(D3×C29)⋊(C7×C25)
unambiguous semidirect product(D3×C25×C29)⋊C7

Splittings

Fitting, HallC3×C25×C29 ⋊ C2×C7
derived, HallC3×C29 ⋊ C2×C7×C25
HallC3×C25×C29⋊C7 ⋊ C2
HallD3×C25×C29 ⋊ C7
HallC25×C29 ⋊ D3×C7
HallC3×C29⋊C7 ⋊ C2×C25
HallD3×C29 ⋊ C7×C25
HallC3×C25 ⋊ C2×C29⋊C7
SylowC29 ⋊ D3×C7×C25
SylowC3 ⋊ C2×C25×C29⋊C7

Subgroups

subgroupG/H
center, hypercenterC25D3×C29⋊C7
commutator, hypocenterC3×C29C2×C7×C25
FrattiniC5C5×D3×C29⋊C7
FittingC3×C25×C29C2×C7
socle, cosocleC3×C5×C29C2×C5×C7
prime radicalC5×D3×C29⋊C7C5
LCSG ▷ C3×C29
UCSC1 ◁ C25

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2175

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 22);