Finite Group Databasebeta

← Prev (#36344914) Next (#36344916) →

C5×C9×#92150 #36344915

order21780
isoclinismisoclinic class of #92150
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C11

Aliases

direct productC5×C9×#92150

Splittings

Fitting, HallC5×C9×C112 ⋊ C4
derived, SylowC112 ⋊ C4×C5×C9
HallC9×C112 ⋊ C4×C5
HallC5×C112 ⋊ C4×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9#92150
commutator, hypocenterC112C4×C5×C9
FrattiniC3C3×C5×#92150
FittingC5×C9×C112C4
socleC3×C5×C112C3×C4
prime radicalC3×C5×C11⋊D11C2×C3
cosocleC3×C11⋊D11C2×C3×C5
LCSG ▷ C112
UCSC1 ◁ C5×C9

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1530 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 264);