Finite Group Databasebeta

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C22×C4×C9×C81 #72190123

order11664
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5038848
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C9

Aliases

abelianC22×C4×C9×C81
multiplicative(ℤ/15485)ˣ, (ℤ/18093)ˣ, (ℤ/22005)ˣ, (ℤ/23085)ˣ, (ℤ/24124)ˣ, (ℤ/30970)ˣ, (ℤ/35964)ˣ, (ℤ/36186)ˣ, (ℤ/44010)ˣ, (ℤ/46170)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C27C23×C32
socle, prime radicalC23×C32C2×C3×C27
LCSG ▷ C1
UCSC1 ◁ G

1323 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11664 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C8×C9×C81, C2×C42×C9×C81, C23×C4×C9×C81
maximal normal subgroup ofC22×C8×C9×C81, C2×C42×C9×C81, C23×C4×C9×C81
maximal quotient ofC22×C8×C9×C81, C2×C42×C9×C81, C23×C4×C9×C81
automorphism group ofC5×C19×C163, C5×C27×C163, C5×C19×C243
outer automorphism group ofC5×C19×C163, C5×C27×C163, C5×C19×C243

GAP

Past the SmallGroups library coverage — no SmallGroups id.