Finite Group Databasebeta

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C3×C7×C162 #72184683

order5376
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 294912
homologyAbelianization (H1) = G · Schur multiplier (H2) = C16

Aliases

abelianC3×C7×C162
multiplicative(ℤ/5729)ˣ, (ℤ/11458)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC82C22×C3×C7
socle, prime radicalC22×C3×C7C82
LCSG ▷ C1
UCSC1 ◁ G

332 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5376 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C7×C16×C32, C2×C3×C7×C162, C7×C9×C162, …
maximal normal subgroup ofC3×C7×C16×C32, C2×C3×C7×C162, C7×C9×C162, …
maximal quotient ofC3×C7×C16×C32, C2×C3×C7×C162, C7×C9×C162, …
automorphism group ofC17×C337
outer automorphism group ofC17×C337

GAP

Past the SmallGroups library coverage — no SmallGroups id.