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C11×C17×C11⋊C5 #23779807

order10285
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC11×C17×C11⋊C5
unambiguous semidirect productC11⋊(C5×C11×C17)
unambiguous semidirect product(C11×C17)⋊(C5×C11)

Splittings

Fitting, socle, HallC112×C17 ⋊ C5
derivedC11 ⋊ C5×C11×C17
SylowC112 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC11×C17C11⋊C5
commutator, cosocle, hypocenterC11C5×C11×C17
FrattiniC1G
Fitting, socleC112×C17C5
LCSG ▷ C11
UCSC1 ◁ C11×C17

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1309 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×D17×C11⋊C5, C11×C17×AGL(1,𝔽11), C11×C17⋊AGL(1,𝔽11), …
maximal normal subgroup ofC11×D17×C11⋊C5, C11×C17×AGL(1,𝔽11), C11×C17⋊AGL(1,𝔽11), …
maximal quotient ofC2×C11×C17×C11⋊C5, C3×C11×C17×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10285, 5);