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C7×C11⋊(D19⋊C3) #22578627

order8778
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊(D19⋊C3)
unambiguous semidirect productC11⋊(C7×D19⋊C3)
unambiguous semidirect product(C19⋊C3)⋊(C7×D11)
unambiguous semidirect productD209⋊(C3×C7)

Splittings

Fitting, socle, HallC7×C11×C19 ⋊ C2×C3
derived, HallC11×C19 ⋊ C2×C3×C7
HallC7×C11×C19⋊C3 ⋊ C2
HallC7×D209 ⋊ C3
HallC11×C19⋊C3 ⋊ C2×C7
HallD209 ⋊ C3×C7
HallC7×C19⋊C3 ⋊ D11
HallC7×C19 ⋊ C3×D11
HallC7×C11 ⋊ D19⋊C3
HallC19⋊C3 ⋊ C7×D11
SylowC19 ⋊ C3×C7×D11
SylowC11 ⋊ C7×D19⋊C3

Subgroups

subgroupG/H
center, hypercenterC7C11⋊(D19⋊C3)
commutator, hypocenterC11×C19C2×C3×C7
FrattiniC1G
Fitting, socleC7×C11×C19C2×C3
LCSG ▷ C11×C19
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

378 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×D11×D19⋊C3, D7×C11⋊(D19⋊C3), ((C19⋊C3)⋊D7)⋊D11, …
maximal normal subgroup ofC7×D11×D19⋊C3, D7×C11⋊(D19⋊C3), ((C19⋊C3)⋊D7)⋊D11, …
maximal quotient ofC7×C11⋊((C19⋊C3)⋊C4), C2×C7×C11⋊(D19⋊C3), C7×C11⋊(#4294⋊C2), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8778, 29);