Finite Group Databasebeta

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C2×C11×C13×C27 #72186643

order7722
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C3×C4×C5×C9 (order 2160) · Inn(G) = C1 · Out(G) = C22×C3×C4×C5×C9
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC7722
abelianC2×C11×C13×C27
multiplicative(ℤ/7723)ˣ, (ℤ/15446)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C2×C3×C11×C13
socle, prime radicalC2×C3×C11×C13C9
LCSG ▷ C1
UCSC1 ◁ G

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7722 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofDic7722, D15444
maximal subgroup ofC4×C11×C13×C27, C22×C11×C13×C27, C2×C11×C13×C81, …
maximal normal subgroup ofC4×C11×C13×C27, C22×C11×C13×C27, C2×C11×C13×C81, …
maximal quotient ofC4×C11×C13×C27, C22×C11×C13×C27, C2×C11×C13×C81, …
automorphism group ofC7723
outer automorphism group ofC7723

GAP

Past the SmallGroups library coverage — no SmallGroups id.