Finite Group Databasebeta

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C22×C3×C8×C9×C11 #72188244

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 414720
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C8×C9×C11
multiplicative(ℤ/11753)ˣ, (ℤ/11837)ˣ, (ℤ/14673)ˣ, (ℤ/15111)ˣ, (ℤ/15219)ˣ, (ℤ/16821)ˣ, (ℤ/19564)ˣ, (ℤ/23506)ˣ, (ℤ/23674)ˣ, (ℤ/29346)ˣ, (ℤ/30222)ˣ, (ℤ/30438)ˣ, (ℤ/33642)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C4C23×C32×C11
socle, prime radicalC23×C32×C11C3×C4
LCSG ▷ C1
UCSC1 ◁ G

760 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C9×C11×C16, C2×C3×C4×C8×C9×C11, C23×C3×C8×C9×C11, …
maximal normal subgroup ofC22×C3×C9×C11×C16, C2×C3×C4×C8×C9×C11, C23×C3×C8×C9×C11, …
maximal quotient ofC22×C3×C9×C11×C16, C2×C3×C4×C8×C9×C11, C23×C3×C8×C9×C11, …
automorphism group ofC7×C23×C73, C7×C19×C89, C7×C27×C89
outer automorphism group ofC7×C23×C73, C7×C19×C89, C7×C27×C89

GAP

Past the SmallGroups library coverage — no SmallGroups id.