Finite Group Databasebeta

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C3×C16×C64 #72182802

order3072
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 131072
homologyAbelianization (H1) = G · Schur multiplier (H2) = C16

Aliases

abelianC3×C16×C64
multiplicative(ℤ/3281)ˣ, (ℤ/6562)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C32C22×C3
socle, prime radicalC22×C3C8×C32
LCSG ▷ C1
UCSC1 ◁ G

290 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C16×C128, C3×C32×C64, C2×C3×C16×C64, …
maximal normal subgroup ofC3×C16×C128, C3×C32×C64, C2×C3×C16×C64, …
maximal quotient ofC3×C16×C128, C3×C32×C64, C2×C3×C16×C64, …
automorphism group ofC17×C193, C2×C17×C193
outer automorphism group ofC17×C193, C2×C17×C193

GAP

Past the SmallGroups library coverage — no SmallGroups id.