Finite Group Databasebeta

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C2×C42×C7×C27 #72185230

order6048
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 165888
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C42×C7×C27
multiplicative(ℤ/9483)ˣ, (ℤ/11355)ˣ, (ℤ/11745)ˣ, (ℤ/12112)ˣ, (ℤ/12644)ˣ, (ℤ/15140)ˣ, (ℤ/18966)ˣ, (ℤ/22710)ˣ, (ℤ/23490)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C9C23×C3×C7
socle, prime radicalC23×C3×C7C22×C9
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C4×C7×C8×C27, C43×C7×C27, C22×C42×C7×C27, …
maximal normal subgroup ofC2×C4×C7×C8×C27, C43×C7×C27, C22×C42×C7×C27, …
maximal quotient ofC2×C4×C7×C8×C27, C43×C7×C27, C22×C42×C7×C27, …
automorphism group ofC3×C29×C109, C5×C29×C81, C2×C5×C29×C81
outer automorphism group ofC3×C29×C109, C5×C29×C81, C2×C5×C29×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.