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C5×C11⋊#64418 #30633544

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

Aliases

direct productC5×C11⋊#64418

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ D3
derived, HallC11×#3862 ⋊ C2×C5
HallC5×C11×#3862 ⋊ C2
HallC5×#3862 ⋊ D11
HallC72×C11 ⋊ C5×D3
HallC5×C72 ⋊ D33
Hall#3862 ⋊ C5×D11
HallC5×C11 ⋊ #64418
SylowC72 ⋊ C5×D33
SylowC11 ⋊ C5×#64418

Subgroups

subgroupG/H
center, hypercenterC5C11⋊#64418
commutator, cosocle, hypocenterC11×#3862C2×C5
FrattiniC1G
Fitting, socleC5×C72×C11D3
LCSG ▷ C11×#3862
UCSC1 ◁ C5

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×D11×#64418, C5×#64418⋊D11, C5×#20266354, …
maximal normal subgroup ofC5×D11×#64418, C5×#64418⋊D11, C5×#20266354, …
maximal quotient ofC5×C11⋊#10596868, C2×C5×C11⋊#64418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 89);