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C2×C9×D17×C59 #49115648

order36108
automorphism?
homologyAbelianization (H1) = C22×C9×C59 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×D17×C59
unambiguous semidirect productC17⋊(C22×C9×C59)
unambiguous semidirect product(C2×C17)⋊(C2×C9×C59)

Splittings

FittingC2×C9×C17×C59 ⋊ C2
derived, SylowC17 ⋊ C22×C9×C59
HallC9×C17×C59 ⋊ C22
HallC17×C59 ⋊ C22×C9
HallC9×C17 ⋊ C22×C59

Subgroups

subgroupG/H
center, hypercenterC2×C9×C59D17
commutator, hypocenterC17C22×C9×C59
FrattiniC3C2×C3×D17×C59
FittingC2×C9×C17×C59C2
socleC2×C3×C17×C59C2×C3
prime radicalC2×C3×D17×C59C3
cosocleC3×C17C22×C3×C59
LCSG ▷ C17
UCSC1 ◁ C2×C9×C59

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18054

Conjugacy classes & character table

10620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36108, 27);