Finite Group Databasebeta

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C2×C11×C243 #72184658

order5346
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C5×C81 (order 1620) · Inn(G) = C1 · Out(G) = C22×C5×C81
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC5346
abelianC2×C11×C243
multiplicative(ℤ/5347)ˣ, (ℤ/10694)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC81C2×C3×C11
socle, prime radicalC2×C3×C11C81
LCSG ▷ C1
UCSC1 ◁ G

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5346 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C11×C243, C22×C11×C243, C2×C11×C729, …
maximal normal subgroup ofC4×C11×C243, C22×C11×C243, C2×C11×C729, …
maximal quotient ofC4×C11×C243, C22×C11×C243, C2×C11×C729, …
automorphism group ofC5347, C2×C5347
outer automorphism group ofC5347, C2×C5347

GAP

Past the SmallGroups library coverage — no SmallGroups id.