Finite Group Databasebeta

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C25×D67⋊C9 #44474601

order30150
automorphism?
homologyAbelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC25×D67⋊C9
unambiguous semidirect productD67⋊(C9×C25)
unambiguous semidirect product(C67⋊C9)⋊(C2×C25)
unambiguous semidirect product(C25×D67)⋊C9

Splittings

derived, SylowC67 ⋊ C2×C9×C25
HallC25×C67⋊C9 ⋊ C2
HallC25×D67 ⋊ C9
HallC25×C67 ⋊ C2×C9
HallC67⋊C9 ⋊ C2×C25
HallD67 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC3×C25D67⋊C3
commutator, hypocenterC67C2×C9×C25
FrattiniC3×C5C5×D67⋊C3
FittingC3×C25×C67C2×C3
socle, cosocleC3×C5×C67C2×C3×C5
prime radicalC3×C5×D67C3×C5
LCSG ▷ C67
UCSC1 ◁ C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15075

Conjugacy classes & character table

1275 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30150, 10);