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C11×C5⋊#64418 #30633565

order16170
automorphism?
homologyAbelianization (H1) = C2×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C5⋊#64418
unambiguous semidirect productC5⋊(C11×#64418)

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ D3
derived, HallC5×#3862 ⋊ C2×C11
HallC5×C11×#3862 ⋊ C2
HallC11×#3862 ⋊ D5
HallC72×C11 ⋊ D15
HallC5×C72 ⋊ D3×C11
Hall#3862 ⋊ D5×C11
HallC5×C11 ⋊ #64418
SylowC72 ⋊ C11×D15
SylowC5 ⋊ C11×#64418

Subgroups

subgroupG/H
center, hypercenterC11C5⋊#64418
commutator, cosocle, hypocenterC5×#3862C2×C11
FrattiniC1G
Fitting, socleC5×C72×C11D3
LCSG ▷ C5×#3862
UCSC1 ◁ C11

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 770

Conjugacy classes & character table

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

Relationships

maximal subgroup ofD11×C5⋊#64418, D5×C11×#64418, D55⋊#64418, …
maximal normal subgroup ofD11×C5⋊#64418, D5×C11×#64418, D55⋊#64418, …
maximal quotient ofC11×#15668724, C2×C11×C5⋊#64418

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 110);