Finite Group Databasebeta

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C42×C7×C8×C11 #72188562

order9856
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5898240
homologyAbelianization (H1) = G · Schur multiplier (H2) = C43

Aliases

abelianC42×C7×C8×C11
multiplicative(ℤ/12905)ˣ, (ℤ/25810)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C4C23×C7×C11
socle, prime radicalC23×C7×C11C22×C4
LCSG ▷ C1
UCSC1 ◁ G

816 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9856 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC42×C7×C11×C16, C4×C7×C82×C11, C2×C42×C7×C8×C11, …
maximal normal subgroup ofC42×C7×C11×C16, C4×C7×C82×C11, C2×C42×C7×C8×C11, …
maximal quotient ofC42×C7×C11×C16, C4×C7×C82×C11, C2×C42×C7×C8×C11, …
automorphism group ofC5×C29×C89
outer automorphism group ofC5×C29×C89

GAP

Past the SmallGroups library coverage — no SmallGroups id.