Finite Group Databasebeta

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C5×C5⋊(D43⋊C9) #34084044

order19350
automorphism?
homologyAbelianization (H1) = C2×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C5⋊(D43⋊C9)
unambiguous semidirect productC5⋊(C5×D43⋊C9)
unambiguous semidirect product(C43⋊C9)⋊(C5×D5)
unambiguous semidirect productD215⋊(C5×C9)
unambiguous semidirect product(C5×D215)⋊C9

Splittings

derivedC5×C43 ⋊ C2×C5×C9
HallC52×C43⋊C9 ⋊ C2
HallC5×D215 ⋊ C9
HallC52×C43 ⋊ C2×C9
HallC43⋊C9 ⋊ C5×D5
SylowC43 ⋊ C5×C9×D5
SylowC52 ⋊ D43⋊C9

Subgroups

subgroupG/H
center, hypercenterC3×C5C5⋊(D43⋊C3)
commutator, hypocenterC5×C43C2×C5×C9
FrattiniC3C5×C5⋊(D43⋊C3)
Fitting, socleC3×C52×C43C2×C3
prime radicalC3×C5×D215C3
cosocleC3×C5×C43C2×C3×C5
LCSG ▷ C5×C43
UCSC1 ◁ C3×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3870

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19350, 35);