Finite Group Databasebeta

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C3×C4×C8×C9×C16 #72192022

order13824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 113246208
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3×C42×C8

Aliases

abelianC3×C4×C8×C9×C16
multiplicative(ℤ/16133)ˣ, (ℤ/32266)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4×C8C23×C32
socle, prime radicalC23×C32C2×C3×C4×C8
LCSG ▷ C1
UCSC1 ◁ G

5460 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C8×C9×C32, C3×C4×C9×C162, C3×C82×C9×C16, …
maximal normal subgroup ofC3×C4×C8×C9×C32, C3×C4×C9×C162, C3×C82×C9×C16, …
maximal quotient ofC3×C4×C8×C9×C32, C3×C4×C9×C162, C3×C82×C9×C16, …
automorphism group ofC13×C17×C73
outer automorphism group ofC13×C17×C73

GAP

Past the SmallGroups library coverage — no SmallGroups id.