Finite Group Databasebeta

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C4×C9×C11×C16 #72185487

order6336
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15360
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC4×C9×C11×C16
multiplicative(ℤ/6749)ˣ, (ℤ/13498)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C8C22×C3×C11
socle, prime radicalC22×C3×C11C2×C3×C8
LCSG ▷ C1
UCSC1 ◁ G

174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6336 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C9×C11×C32, C8×C9×C11×C16, C2×C4×C9×C11×C16, …
maximal normal subgroup ofC4×C9×C11×C32, C8×C9×C11×C16, C2×C4×C9×C11×C16, …
maximal quotient ofC4×C9×C11×C32, C8×C9×C11×C16, C2×C4×C9×C11×C16, …
automorphism group ofC17×C397
outer automorphism group ofC17×C397

GAP

Past the SmallGroups library coverage — no SmallGroups id.