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C5×C11×#64422 #30633535

order16170
isoclinismisoclinic class of #64422
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×#64422

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C2×C3
derived, SylowC72 ⋊ C2×C3×C5×C11
HallC5×C11×#3862 ⋊ C2
HallC5×C7×C11×D7 ⋊ C3
HallC11×#3862 ⋊ C2×C5
HallC7×C11×D7 ⋊ C3×C5
HallC5×#3862 ⋊ C2×C11
HallC72×C11 ⋊ C2×C3×C5
HallC5×C7×D7 ⋊ C3×C11
HallC5×C72 ⋊ C2×C3×C11
Hall#3862 ⋊ C2×C5×C11
HallC7×D7 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC5×C11#64422
commutator, cosocle, hypocenterC72C2×C3×C5×C11
FrattiniC1G
Fitting, socleC5×C72×C11C2×C3
LCSG ▷ C72
UCSC1 ◁ C5×C11

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

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

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 80);