Finite Group Databasebeta

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C22×C7×C8×C47 #72189134

order10528
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 105984
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C7×C8×C47
multiplicative(ℤ/21064)ˣ, (ℤ/21088)ˣ, (ℤ/31596)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C23×C7×C47
socle, prime radicalC23×C7×C47C4
LCSG ▷ C1
UCSC1 ◁ G

152 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C7×C16×C47, C2×C4×C7×C8×C47, C23×C7×C8×C47, …
maximal normal subgroup ofC22×C7×C16×C47, C2×C4×C7×C8×C47, C23×C7×C8×C47, …
maximal quotient ofC22×C7×C16×C47, C2×C4×C7×C8×C47, C23×C7×C8×C47, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.