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C22×C3×C11×C83 #24926579

order10956
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9840
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC22×C3×C11×C83
multiplicative(ℤ/11189)ˣ, (ℤ/11477)ˣ, (ℤ/16437)ˣ, (ℤ/21916)ˣ, (ℤ/22378)ˣ, (ℤ/22954)ˣ, (ℤ/32874)ˣ

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10956 conjugacy classes. The character table is too large to display.

Relationships

Fitting subgroup ofC11×C22⋊C9×C83, C3×C11×A4×C83
socle ofC22×C9×C11×C83, C11×C22⋊C9×C83, C3×C11×A4×C83
maximal subgroup ofC22×C9×C11×C83, C11×C22⋊C9×C83, C22×C32×C11×C83, …
maximal normal subgroup ofC22×C9×C11×C83, C11×C22⋊C9×C83, C22×C32×C11×C83, …
maximal quotient ofC22×C9×C11×C83, C22×C32×C11×C83, C2×C3×D3×C11×C83, …
automorphism group ofC67×C167, C23×C499
outer automorphism group ofC67×C167, C23×C499

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10956, 9);