Finite Group Databasebeta

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C25×C29×D21 #44478529

order30450
automorphism?
homologyAbelianization (H1) = C2×C25×C29 · Schur multiplier (H2) = C1

Aliases

direct productC25×C29×D21
unambiguous semidirect productC3⋊(D7×C25×C29)
unambiguous semidirect productC7⋊(D3×C25×C29)

Splittings

Fitting, HallC3×C7×C25×C29 ⋊ C2
derived, HallC3×C7 ⋊ C2×C25×C29
HallC7×C25×C29 ⋊ D3
HallC3×C25×C29 ⋊ D7
HallC3×C7×C29 ⋊ C2×C25
HallC3×C7×C25 ⋊ C2×C29
HallC7×C29 ⋊ D3×C25
HallC7×C25 ⋊ D3×C29
HallC3×C29 ⋊ D7×C25
HallC3×C25 ⋊ D7×C29
SylowC7 ⋊ D3×C25×C29
SylowC3 ⋊ D7×C25×C29

Subgroups

subgroupG/H
center, hypercenterC25×C29D21
commutator, hypocenterC3×C7C2×C25×C29
FrattiniC5C5×C29×D21
FittingC3×C7×C25×C29C2
socleC3×C5×C7×C29C2×C5
prime radicalC5×C29×D21C5
cosocleC3×C5×C7C2×C5×C29
LCSG ▷ C3×C7
UCSC1 ◁ C25×C29

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15225

Conjugacy classes & character table

8700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 13);