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C71×(C5⋊D5)⋊C9 #44544038

order31950
automorphism?
homologyAbelianization (H1) = C2×C9×C71 · Schur multiplier (H2) = C5

Aliases

direct productC71×(C5⋊D5)⋊C9
unambiguous semidirect product(C5⋊D5)⋊(C9×C71)
unambiguous semidirect product(C5⋊D5×C71)⋊C9

Splittings

derived, SylowC52 ⋊ C2×C9×C71
HallC71×C52⋊C9 ⋊ C2
HallC5⋊D5×C71 ⋊ C9
HallC52×C71 ⋊ C2×C9
HallC52⋊C9 ⋊ C2×C71
HallC5⋊D5 ⋊ C9×C71

Subgroups

subgroupG/H
center, hypercenterC3×C71(C5⋊D5)⋊C3
commutator, hypocenterC52C2×C9×C71
FrattiniC3C71×(C5⋊D5)⋊C3
Fitting, socleC3×C52×C71C2×C3
prime radicalC3×C5⋊D5×C71C3
cosocleC3×C52C2×C3×C71
LCSG ▷ C52
UCSC1 ◁ C3×C71

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3195

Conjugacy classes & character table

2130 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31950, 41);