Finite Group Databasebeta

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C24×C7×C53 #72185147

order5936
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6289920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C7×C53
multiplicative(ℤ/17832)ˣ

Subgroups

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

268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5936 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C7×C53, C25×C7×C53, C24×C3×C7×C53, …
maximal normal subgroup ofC23×C4×C7×C53, C25×C7×C53, C24×C3×C7×C53, …
maximal quotient ofC23×C4×C7×C53, C25×C7×C53, C24×C3×C7×C53, …
automorphism group ofC3×C8×C743
outer automorphism group ofC3×C8×C743

GAP

Past the SmallGroups library coverage — no SmallGroups id.