Finite Group Databasebeta

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C22×C3×C27×C29 #72188155

order9396
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 54432
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C27×C29
multiplicative(ℤ/10969)ˣ, (ℤ/14103)ˣ, (ℤ/21938)ˣ, (ℤ/28206)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C22×C32×C29
socle, prime radicalC22×C32×C29C9
LCSG ▷ C1
UCSC1 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9396 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C27×C29, C23×C3×C27×C29, C22×C3×C29×C81, …
maximal normal subgroup ofC2×C3×C4×C27×C29, C23×C3×C27×C29, C22×C3×C29×C81, …
maximal quotient ofC2×C3×C4×C27×C29, C23×C3×C27×C29, C22×C3×C29×C81, …
automorphism group ofC7×C1567
outer automorphism group ofC7×C1567

GAP

Past the SmallGroups library coverage — no SmallGroups id.