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C43×(C5⋊D5)⋊C9 #34084050

order19350
automorphism?
homologyAbelianization (H1) = C2×C9×C43 · Schur multiplier (H2) = C5

Aliases

direct productC43×(C5⋊D5)⋊C9
unambiguous semidirect product(C5⋊D5)⋊(C9×C43)

Splittings

derived, SylowC52 ⋊ C2×C9×C43
HallC43×C52⋊C9 ⋊ C2
HallC43×C5⋊D5 ⋊ C9
HallC52×C43 ⋊ C2×C9
HallC52⋊C9 ⋊ C2×C43
HallC5⋊D5 ⋊ C9×C43

Subgroups

subgroupG/H
center, hypercenterC3×C43(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C9×C43
FrattiniC3C43×(C5⋊D5)⋊C3
Fitting, socleC3×C52×C43C2×C3
prime radicalC3×C43×C5⋊D5C3
cosocleC3×C52C2×C3×C43
LCSG ▷ C52
UCSC1 ◁ C3×C43

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1935

Conjugacy classes & character table

1290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19350, 41);