Finite Group Databasebeta

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C11×C16×C47 #72187203

order8272
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C23×C4×C5×C23 (order 3680) · Inn(G) = C1 · Out(G) = C23×C4×C5×C23
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC8272
abelianC11×C16×C47
multiplicative(ℤ/8273)ˣ, (ℤ/16546)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C2×C11×C47
socle, prime radicalC2×C11×C47C8
LCSG ▷ C1
UCSC1 ◁ G

20 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8272 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic8272, D16544
maximal subgroup ofC11×C32×C47, C2×C11×C16×C47, C3×C11×C16×C47, …
maximal normal subgroup ofC11×C32×C47, C2×C11×C16×C47, C3×C11×C16×C47, …
maximal quotient ofC11×C32×C47, C2×C11×C16×C47, C3×C11×C16×C47
automorphism group ofC8273
outer automorphism group ofC8273

GAP

Past the SmallGroups library coverage — no SmallGroups id.