Finite Group Databasebeta

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C24×C3×C5×C47 #72189795

order11280
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7418880
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C3×C5×C47
multiplicative(ℤ/24904)ˣ, (ℤ/37356)ˣ

Subgroups

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

536 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11280 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C5×C47, C25×C3×C5×C47
maximal normal subgroup ofC23×C3×C4×C5×C47, C25×C3×C5×C47
maximal quotient ofC23×C3×C4×C5×C47, C25×C3×C5×C47
automorphism group ofC8×C11×C283
outer automorphism group ofC8×C11×C283

GAP

Past the SmallGroups library coverage — no SmallGroups id.