Finite Group Databasebeta

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C2×D5×C112⋊C9 #36344909

order21780
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C11

Aliases

direct productC2×D5×C112⋊C9
unambiguous semidirect productC5⋊(C22×C112⋊C9)
unambiguous semidirect product(C2×C5)⋊(C2×C112⋊C9)
unambiguous semidirect product(C2×D5×C112)⋊C9

Splittings

derived, HallC5×C112 ⋊ C22×C9
HallC5×C112⋊C9 ⋊ C22
HallC2×D5×C112 ⋊ C9
SylowC112 ⋊ C2×C9×D5
SylowC5 ⋊ C22×C112⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3D5×C112⋊C3
commutator, hypocenterC5×C112C22×C9
FrattiniC3C2×D5×C112⋊C3
Fitting, socleC2×C3×C5×C112C2×C3
prime radicalC2×C3×D5×C112C3
cosocleC3×C5×C112C22×C3
LCSG ▷ C5×C112
UCSC1 ◁ C2×C3

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1032 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21780, 258);