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C2×C5×C11×C7⋊C9 #20294116

order6930
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C11×C7⋊C9
unambiguous semidirect product(C2×C7)⋊(C5×C9×C11)
unambiguous semidirect product(C2×C5×C7)⋊(C9×C11)
unambiguous semidirect product(C2×C5×C7×C11)⋊C9

Splittings

derived, SylowC7 ⋊ C2×C5×C9×C11
HallC2×C5×C7×C11 ⋊ C9
HallC5×C7×C11 ⋊ C2×C9
HallC2×C7×C11 ⋊ C5×C9
HallC7×C11 ⋊ C2×C5×C9
HallC2×C5×C7 ⋊ C9×C11
HallC5×C7 ⋊ C2×C9×C11
HallC2×C7 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C11ΓL(1,𝔽8)
commutator, hypocenterC7C2×C5×C9×C11
FrattiniC3C2×C5×C11×ΓL(1,𝔽8)
Fitting, socleC2×C3×C5×C7×C11C3
LCSG ▷ C7
UCSC1 ◁ C2×C3×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1650 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C11×C7⋊C9, C5×Dic11×C7⋊C9, C5×C11×Dic7⋊C9, …
maximal normal subgroup ofC4×C5×C11×C7⋊C9, C5×Dic11×C7⋊C9, C5×C11×Dic7⋊C9, …
maximal quotient ofC4×C5×C11×C7⋊C9, C22×C5×C11×C7⋊C9, C2×C11×C25×C7⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 3);