Finite Group Databasebeta

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C29×D525 #44478533

order30450
automorphism?
homologyAbelianization (H1) = C2×C29 · Schur multiplier (H2) = C1

Aliases

direct productC29×D525
unambiguous semidirect productC3⋊(C29×D175)
unambiguous semidirect productC7⋊(C29×D75)
unambiguous semidirect productC25⋊(C29×D21)

Splittings

Fitting, HallC3×C7×C25×C29 ⋊ C2
derived, HallC3×C7×C25 ⋊ C2×C29
HallC7×C25×C29 ⋊ D3
HallC3×C25×C29 ⋊ D7
HallC25×C29 ⋊ D21
HallC3×C7×C29 ⋊ D25
HallC7×C29 ⋊ D75
HallC7×C25 ⋊ D3×C29
HallC3×C29 ⋊ D175
HallC3×C25 ⋊ D7×C29
SylowC25 ⋊ C29×D21
HallC3×C7 ⋊ C29×D25
SylowC7 ⋊ C29×D75
SylowC3 ⋊ C29×D175

Subgroups

subgroupG/H
center, hypercenterC29D525
commutator, cosocle, hypocenterC3×C7×C25C2×C29
FrattiniC5C29×D105
FittingC3×C7×C25×C29C2
socleC3×C5×C7×C29D5
LCSG ▷ C3×C7×C25
UCSC1 ◁ C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15225

Conjugacy classes & character table

7656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 17);