Finite Group Databasebeta

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C43×C7×C27 #72190486

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9289728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C43

Aliases

abelianC43×C7×C27
multiplicative(ℤ/15805)ˣ, (ℤ/31610)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C9C23×C3×C7
socle, prime radicalC23×C3×C7C23×C9
LCSG ▷ C1
UCSC1 ◁ G

1032 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C7×C8×C27, C2×C43×C7×C27
maximal normal subgroup ofC42×C7×C8×C27, C2×C43×C7×C27
maximal quotient ofC42×C7×C8×C27, C2×C43×C7×C27
automorphism group ofC5×C29×C109
outer automorphism group ofC5×C29×C109

GAP

Past the SmallGroups library coverage — no SmallGroups id.