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C22×C11×C49⋊C3 #20266290

order6468
isoclinismisoclinic class of C49⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C11 · Schur multiplier (H2) = C2

Aliases

direct productC22×C11×C49⋊C3

Splittings

Fitting, HallC22×C11×C49 ⋊ C3
derived, SylowC49 ⋊ C22×C3×C11
HallC11×C49 ⋊ C22×C3
HallC22×C49 ⋊ C3×C11

Subgroups

subgroupG/H
center, hypercenterC22×C11C49⋊C3
commutator, hypocenterC49C22×C3×C11
FrattiniC7C22×C11×ΓL(1,𝔽8)
FittingC22×C11×C49C3
socleC22×C7×C11ΓL(1,𝔽8)
LCSG ▷ C49
UCSC1 ◁ C22×C11

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

836 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×A4×C49⋊C3, C2×D3×C11×C49⋊C3, C22×C3×C11×C49⋊C3, …
maximal normal subgroup ofC11×A4×C49⋊C3, C22×C3×C11×C49⋊C3, C22×C11⋊C5×C49⋊C3, …
maximal quotient ofC22×C11×C49⋊C9, C2×D3×C11×C49⋊C3, C22×C3×C11×C49⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6468, 25);