Finite Group Databasebeta

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C5×C9×D112 #36344914

order21780
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×C9×D112

Splittings

Fitting, HallC5×C9×C112 ⋊ C22
derived, SylowC112 ⋊ C22×C5×C9
HallC9×C112 ⋊ C22×C5
HallC5×C112 ⋊ C22×C9

Subgroups

subgroupG/H
center, hypercenterC5×C9D112
commutator, hypocenterC112C22×C5×C9
FrattiniC3C3×C5×D112
FittingC5×C9×C112C22
socleC3×C5×C112C22×C3
prime radicalC3×C5×D112C3
cosocleC3×C112C22×C3×C5
LCSG ▷ C112
UCSC1 ◁ C5×C9

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2205 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 263);