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C23×C5×C9×C17 #72185282

order6120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 64512
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C5×C9×C17
multiplicative(ℤ/10131)ˣ, (ℤ/12248)ˣ, (ℤ/13508)ˣ, (ℤ/18372)ˣ, (ℤ/20262)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C23×C3×C5×C17
socle, prime radicalC23×C3×C5×C17C3
LCSG ▷ C1
UCSC1 ◁ G

192 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C9×C17, C24×C5×C9×C17, C23×C5×C17×C27, …
maximal normal subgroup ofC22×C4×C5×C9×C17, C24×C5×C9×C17, C23×C5×C17×C27, …
maximal quotient ofC22×C4×C5×C9×C17, C24×C5×C9×C17, C23×C5×C17×C27, …
automorphism group ofC3×C11×C307
outer automorphism group ofC3×C11×C307

GAP

Past the SmallGroups library coverage — no SmallGroups id.