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C7×C9×D5×C11 #20294121

order6930
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C2×C7×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C9×D5×C11
unambiguous semidirect productC5⋊(C2×C7×C9×C11)

Splittings

Fitting, HallC5×C7×C9×C11 ⋊ C2
derived, SylowC5 ⋊ C2×C7×C9×C11
HallC5×C9×C11 ⋊ C2×C7
HallC5×C7×C11 ⋊ C2×C9
HallC5×C7×C9 ⋊ C2×C11
HallC5×C11 ⋊ C2×C7×C9
HallC5×C9 ⋊ C2×C7×C11
HallC5×C7 ⋊ C2×C9×C11

Subgroups

subgroupG/H
center, hypercenterC7×C9×C11D5
commutator, hypocenterC5C2×C7×C9×C11
FrattiniC3C3×C7×D5×C11
FittingC5×C7×C9×C11C2
socleC3×C5×C7×C11C2×C3
LCSG ▷ C5
UCSC1 ◁ C7×C9×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C9×C11×AGL(1,𝔽5), C7×C9×C11⋊AGL(1,𝔽5), C9×C11×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC7×C9×C11×AGL(1,𝔽5), C7×C9×C11⋊AGL(1,𝔽5), C9×C11×C7⋊AGL(1,𝔽5), …
maximal quotient ofC7×C9×C11×Dic5, C2×C7×C9×D5×C11, C7×C9×C11×D25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 8);