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C32×D7×C11⋊C5 #20294161

order6930
automorphism?
homologyAbelianization (H1) = C2×C32×C5 · Schur multiplier (H2) = C3

Aliases

direct productC32×D7×C11⋊C5
unambiguous semidirect product(C32×C11×D7)⋊C5

Splittings

Fitting, socle, HallC32×C7×C11 ⋊ C2×C5
derived, HallC7×C11 ⋊ C2×C32×C5
HallC32×C7×C11⋊C5 ⋊ C2
HallC32×C11×D7 ⋊ C5
HallC7×C11⋊C5 ⋊ C2×C32
HallC11×D7 ⋊ C32×C5
HallC32×C11 ⋊ C5×D7
HallC32×C7 ⋊ C2×C11⋊C5
SylowC11 ⋊ C32×C5×D7
SylowC7 ⋊ C2×C32×C11⋊C5

Subgroups

subgroupG/H
center, hypercenterC32D7×C11⋊C5
commutator, hypocenterC7×C11C2×C32×C5
FrattiniC1G
Fitting, socleC32×C7×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

315 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC32×D7×AGL(1,𝔽11), C3×D7×C3⋊AGL(1,𝔽11), C3×D3×D7×C11⋊C5, …
maximal normal subgroup ofC32×D7×AGL(1,𝔽11), C3×D7×C3⋊AGL(1,𝔽11), C3×D3×D7×C11⋊C5, …
maximal quotient ofC32×Dic7×C11⋊C5, C2×C32×D7×C11⋊C5, C32×D7×C11⋊C25, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6930, 48);