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C5×C11⋊#64422 #30633536

order16170
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊#64422

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, HallC72×C11 ⋊ C2×C3×C5
HallC5×C11×#3862 ⋊ C2
HallC5×C7×D77 ⋊ C3
HallC11×#3862 ⋊ C2×C5
HallC7×D77 ⋊ C3×C5
HallC5×#3862 ⋊ D11
HallC5×C72 ⋊ C3×D11
Hall#3862 ⋊ C5×D11
HallC5×C11 ⋊ #64422
SylowC72 ⋊ C3×C5×D11
SylowC11 ⋊ C5×#64422

Subgroups

subgroupG/H
center, hypercenterC5C11⋊#64422
commutator, cosocle, hypocenterC72×C11C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C72×C11
UCSC1 ◁ C5

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×#64422, C5×#64422⋊D11, C5×#20266343, …
maximal normal subgroup ofC5×D11×#64422, C5×#64422⋊D11, C5×#20266343, …
maximal quotient ofC5×C11⋊#10596872, C2×C5×C11⋊#64422

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 81);