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C4×C9×C101⋊C5 #32911369

order18180
isoclinismisoclinic class of C101⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C9×C101⋊C5
unambiguous semidirect product(C4×C101)⋊(C5×C9)
unambiguous semidirect product(C4×C9×C101)⋊C5

Splittings

Fitting, HallC4×C9×C101 ⋊ C5
derived, SylowC101 ⋊ C4×C5×C9
HallC9×C101 ⋊ C4×C5
HallC4×C101 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC4×C9C101⋊C5
commutator, hypocenterC101C4×C5×C9
FrattiniC2×C3C2×C3×C101⋊C5
FittingC4×C9×C101C5
socle, cosocleC2×C3×C101C2×C3×C5
prime radicalC2×C3×C101⋊C5C2×C3
LCSG ▷ C101
UCSC1 ◁ C4×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3636

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 2);