Finite Group Databasebeta

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C9×C11×D55 #24926125

order10890
isoclinismisoclinic class of D55
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC9×C11×D55
unambiguous semidirect productC5⋊(C9×C11×D11)
unambiguous semidirect productC11⋊(C9×D5×C11)

Splittings

Fitting, HallC5×C9×C112 ⋊ C2
derivedC5×C11 ⋊ C2×C9×C11
HallC9×C112 ⋊ D5
HallC5×C112 ⋊ C2×C9
SylowC112 ⋊ C9×D5
HallC5×C9 ⋊ C11×D11
SylowC5 ⋊ C9×C11×D11

Subgroups

subgroupG/H
center, hypercenterC9×C11D55
commutator, hypocenterC5×C11C2×C9×C11
FrattiniC3C3×C11×D55
FittingC5×C9×C112C2
socleC3×C5×C112C2×C3
prime radicalC3×C11×D55C3
cosocleC3×C5×C11C2×C3×C11
LCSG ▷ C5×C11
UCSC1 ◁ C9×C11

78 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2871 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×D5×C11×D11, C9×D11×D55, C9×D55⋊D11, …
maximal normal subgroup ofC9×D5×C11×D11, C9×D11×D55, C9×D55⋊D11, …
maximal quotient ofC9×C11×Dic55, C2×C9×C11×D55

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10890, 74);