Finite Group Databasebeta

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C23×C42×C27 #72183137

order3456
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1189085184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C42×C27
multiplicative(ℤ/13080)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C9C25×C3
socle, prime radicalC25×C3C22×C9
LCSG ▷ C1
UCSC1 ◁ G

6000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3456 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C8×C27, C22×C43×C27, C24×C42×C27, …
maximal normal subgroup ofC23×C4×C8×C27, C22×C43×C27, C24×C42×C27, …
maximal quotient ofC23×C4×C8×C27, C22×C43×C27, C24×C42×C27, …
automorphism group ofC3×C5×C8×C109
outer automorphism group ofC3×C5×C8×C109

GAP

Past the SmallGroups library coverage — no SmallGroups id.