Finite Group Databasebeta

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C22×C5×C11×C53 #26042913

order11660
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 12480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C5×C11×C53
multiplicative(ℤ/12947)ˣ, (ℤ/25894)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11660 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC5×C11×A4×C53
socle ofC5×C11×A4×C53
maximal subgroup ofC22×C3×C5×C11×C53, C5×C11×A4×C53, C2×C5×D3×C11×C53, …
maximal normal subgroup ofC22×C3×C5×C11×C53, C5×C11×A4×C53, C2×C4×C5×C11×C53, …
maximal quotient ofC22×C3×C5×C11×C53, C2×C5×D3×C11×C53, C2×C4×C5×C11×C53, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11660, 13);