Finite Group Databasebeta

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C42×C5×C9×C11 #72186830

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 23040
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C5×C9×C11
multiplicative(ℤ/9925)ˣ, (ℤ/19850)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C22×C3×C5×C11
socle, prime radicalC22×C3×C5×C11C22×C3
LCSG ▷ C1
UCSC1 ◁ G

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C8×C9×C11, C2×C42×C5×C9×C11, C42×C5×C11×C27, …
maximal normal subgroup ofC4×C5×C8×C9×C11, C2×C42×C5×C9×C11, C42×C5×C11×C27, …
maximal quotient ofC4×C5×C8×C9×C11, C2×C42×C5×C9×C11, C42×C5×C11×C27, …
automorphism group ofC25×C397
outer automorphism group ofC25×C397

GAP

Past the SmallGroups library coverage — no SmallGroups id.