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C9×Dic101⋊C5 #32911377

order18180
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC9×Dic101⋊C5
unambiguous semidirect productDic101⋊(C5×C9)
unambiguous semidirect product(C9×Dic101)⋊C5

Splittings

derived, SylowC101 ⋊ C4×C5×C9
HallC9×C101⋊C5 ⋊ C4
HallC9×Dic101 ⋊ C5
HallC9×C101 ⋊ C4×C5
HallC101⋊C5 ⋊ C4×C9
HallDic101 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C9D101⋊C5
commutator, hypocenterC101C4×C5×C9
FrattiniC2×C3C3×D101⋊C5
FittingC2×C9×C101C2×C5
socle, cosocleC2×C3×C101C2×C3×C5
prime radicalC2×C3×C101⋊C5C2×C3
LCSG ▷ C101
UCSC1 ◁ C2×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3636

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 10);