Finite Group Databasebeta

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C3×C7×C17×C27 #72188359

order9639
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 31104
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C7×C17×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C32×C7×C17
socle, prime radicalC32×C7×C17C9
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9639 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C7×C17×C27, C3×C7×C17×C81, C7×C9×C17×C27, …
maximal normal subgroup ofC2×C3×C7×C17×C27, C3×C7×C17×C81, C7×C9×C17×C27, …
maximal quotient ofC2×C3×C7×C17×C27, C3×C7×C17×C81, C7×C9×C17×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.