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C3×C17×C61⋊C3 #22605388

order9333
isoclinismisoclinic class of C61⋊C3
automorphism?
homologyAbelianization (H1) = C32×C17 · Schur multiplier (H2) = C3

Aliases

direct productC3×C17×C61⋊C3
unambiguous semidirect productC61⋊(C32×C17)
unambiguous semidirect product(C3×C61)⋊(C3×C17)
unambiguous semidirect product(C17×C61)⋊C32
unambiguous semidirect product(C3×C17×C61)⋊C3

Splittings

Fitting, socleC3×C17×C61 ⋊ C3
derived, SylowC61 ⋊ C32×C17
HallC17×C61 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C17C61⋊C3
commutator, hypocenterC61C32×C17
FrattiniC1G
Fitting, socleC3×C17×C61C3
LCSG ▷ C61
UCSC1 ◁ C3×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1173 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C17×D61⋊C3, C3×C17⋊(D61⋊C3), C3×D17×C61⋊C3, …
maximal normal subgroup ofC3×C17×D61⋊C3, C3×C17⋊(D61⋊C3), C3×D17×C61⋊C3, …
maximal quotient ofC2×C3×C17×C61⋊C3, A4×C17×C61⋊C3, C3×C17×C22⋊(C61⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9333, 4);