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C3×C11×C79⋊C3 #21463147

order7821
isoclinismisoclinic class of C79⋊C3
automorphism?
homologyAbelianization (H1) = C32×C11 · Schur multiplier (H2) = C3

Aliases

direct productC3×C11×C79⋊C3
unambiguous semidirect productC79⋊(C32×C11)
unambiguous semidirect product(C3×C79)⋊(C3×C11)
unambiguous semidirect product(C11×C79)⋊C32
unambiguous semidirect product(C3×C11×C79)⋊C3

Splittings

Fitting, socleC3×C11×C79 ⋊ C3
derived, SylowC79 ⋊ C32×C11
HallC11×C79 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C11C79⋊C3
commutator, hypocenterC79C32×C11
FrattiniC1G
Fitting, socleC3×C11×C79C3
LCSG ▷ C79
UCSC1 ◁ C3×C11

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

957 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11×D79⋊C3, C3×C11⋊(D79⋊C3), C3×D11×C79⋊C3, …
maximal normal subgroup ofC3×C11×D79⋊C3, C3×C11⋊(D79⋊C3), C3×D11×C79⋊C3, …
maximal quotient ofC2×C3×C11×C79⋊C3, C11×A4×C79⋊C3, C3×C11×C22⋊(C79⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7821, 4);