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C4×C9×C121⋊C5 #36344656

order21780
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC4×C9×C121⋊C5
unambiguous semidirect product(C4×C121)⋊(C5×C9)
unambiguous semidirect product(C4×C9×C121)⋊C5

Splittings

Fitting, HallC4×C9×C121 ⋊ C5
derived, SylowC121 ⋊ C4×C5×C9
HallC9×C121 ⋊ C4×C5
HallC4×C121 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC4×C9C121⋊C5
commutator, hypocenterC121C4×C5×C9
Frattini, socleC2×C3×C11C2×C3×C11⋊C5
FittingC4×C9×C121C5
prime radicalC2×C3×C121⋊C5C2×C3
cosocleC2×C3×C121C2×C3×C5
LCSG ▷ C121
UCSC1 ◁ C4×C9

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 5);