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C5×C9×#6923 #24926692

order10980
isoclinismisoclinic class of #6923
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×C9×#6923

Splittings

Fitting, HallC5×C9×C61 ⋊ C4
derived, SylowC61 ⋊ C4×C5×C9
HallC9×C61 ⋊ C4×C5
HallC5×C61 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9#6923
commutator, hypocenterC61C4×C5×C9
FrattiniC3C3×C5×#6923
FittingC5×C9×C61C4
socleC3×C5×C61C3×C4
prime radicalC3×C5×D61C2×C3
cosocleC3×D61C2×C3×C5
LCSG ▷ C61
UCSC1 ◁ C5×C9

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

855 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10980, 42);