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C24×C3×C251 #72190447

order12048
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10080000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C3×C251
multiplicative(ℤ/28168)ˣ, (ℤ/36216)ˣ, (ℤ/42252)ˣ

Subgroups

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

268 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC25×C3×C251, C23×C3×C4×C251
maximal normal subgroup ofC25×C3×C251, C23×C3×C4×C251
maximal quotient ofC25×C3×C251, C23×C3×C4×C251
automorphism group ofC7×C8×C503
outer automorphism group ofC7×C8×C503

GAP

Past the SmallGroups library coverage — no SmallGroups id.