Finite Group Databasebeta

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C3×C9×C11×C17 #72184407

order5049
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 17280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C9×C11×C17

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C32×C11×C17
socle, prime radicalC32×C11×C17C3
LCSG ▷ C1
UCSC1 ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5049 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C9×C11×C17, C3×C11×C17×C27, C92×C11×C17, …
maximal normal subgroup ofC2×C3×C9×C11×C17, C3×C11×C17×C27, C92×C11×C17, …
maximal quotient ofC2×C3×C9×C11×C17, C3×C11×C17×C27, C92×C11×C17, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.