Finite Group Databasebeta

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C3×C5×C7×C81 #72187377

order8505
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 23328
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C5×C7×C81

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC27C32×C5×C7
socle, prime radicalC32×C5×C7C27
LCSG ▷ C1
UCSC1 ◁ G

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8505 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C7×C81, C3×C5×C7×C243, C5×C7×C9×C81, …
maximal normal subgroup ofC2×C3×C5×C7×C81, C3×C5×C7×C243, C5×C7×C9×C81, …
maximal quotient ofC2×C3×C5×C7×C81, C3×C5×C7×C243, C5×C7×C9×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.