Finite Group Databasebeta

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C2×C25×C43⋊C9 #34084014

order19350
automorphism?
homologyAbelianization (H1) = C2×C9×C25 · Schur multiplier (H2) = C1

Aliases

direct productC2×C25×C43⋊C9
unambiguous semidirect product(C2×C43)⋊(C9×C25)
unambiguous semidirect product(C2×C25×C43)⋊C9

Splittings

derived, SylowC43 ⋊ C2×C9×C25
HallC2×C25×C43 ⋊ C9
HallC25×C43 ⋊ C2×C9
HallC2×C43 ⋊ C9×C25

Subgroups

subgroupG/H
center, hypercenterC2×C3×C25C43⋊C3
commutator, hypocenterC43C2×C9×C25
FrattiniC3×C5C2×C5×C43⋊C3
FittingC2×C3×C25×C43C3
socle, prime radicalC2×C3×C5×C43C3×C5
cosocleC3×C5×C43C2×C3×C5
LCSG ▷ C43
UCSC1 ◁ C2×C3×C25

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19350

Conjugacy classes & character table

2550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19350, 5);