Finite Group Databasebeta

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C42×C11×C47 #72187205

order8272
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 44160
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C11×C47
multiplicative(ℤ/10345)ˣ, (ℤ/20690)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C11×C47
socle, prime radicalC22×C11×C47C22
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8272 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C8×C11×C47, C2×C42×C11×C47, C3×C42×C11×C47
maximal normal subgroup ofC4×C8×C11×C47, C2×C42×C11×C47, C3×C42×C11×C47
maximal quotient ofC4×C8×C11×C47, C2×C42×C11×C47, C3×C42×C11×C47
automorphism group ofC5×C2069
outer automorphism group ofC5×C2069

GAP

Past the SmallGroups library coverage — no SmallGroups id.