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C5×C11×D7⋊C9 #20294141

order6930
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×D7⋊C9
unambiguous semidirect productD7⋊(C5×C9×C11)
unambiguous semidirect product(C7⋊C9)⋊(C2×C5×C11)
unambiguous semidirect product(C5×D7)⋊(C9×C11)
unambiguous semidirect product(C5×C11×D7)⋊C9

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C11
HallC5×C11×C7⋊C9 ⋊ C2
HallC5×C11×D7 ⋊ C9
HallC11×C7⋊C9 ⋊ C2×C5
HallC5×C7×C11 ⋊ C2×C9
HallC5×C7⋊C9 ⋊ C2×C11
HallC11×D7 ⋊ C5×C9
HallC7×C11 ⋊ C2×C5×C9
HallC5×D7 ⋊ C9×C11
HallC7⋊C9 ⋊ C2×C5×C11
HallC5×C7 ⋊ C2×C9×C11
HallD7 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C5×C11AGL(1,𝔽7)
commutator, hypocenterC7C2×C5×C9×C11
FrattiniC3C5×C11×AGL(1,𝔽7)
Fitting, socleC3×C5×C7×C11C2×C3
LCSG ▷ C7
UCSC1 ◁ C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1155 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D11×D7⋊C9, D5×C11×D7⋊C9, D55×D7⋊C9, …
maximal normal subgroup ofC5×D11×D7⋊C9, D5×C11×D7⋊C9, D55×D7⋊C9, …
maximal quotient ofC5×C11×Dic7⋊C9, C2×C5×C11×D7⋊C9, C11×C25×D7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 28);