Finite Group Databasebeta

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C22×C3×C53×C7 #72189113

order10500
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 107136000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C53

Aliases

abelianC22×C3×C53×C7

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

1280 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10500 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C53×C7, C23×C3×C53×C7, C22×C53×C7×C9, …
maximal normal subgroup ofC2×C3×C4×C53×C7, C23×C3×C53×C7, C22×C53×C7×C9, …
maximal quotient ofC2×C3×C4×C53×C7, C23×C3×C53×C7, C22×C53×C7×C9, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.