Finite Group Databasebeta

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C24×C5×C9×C11 #72186834

order7920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4838400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C5×C9×C11
multiplicative(ℤ/14421)ˣ, (ℤ/17512)ˣ, (ℤ/18392)ˣ, (ℤ/19228)ˣ, (ℤ/23784)ˣ, (ℤ/26136)ˣ, (ℤ/26268)ˣ, (ℤ/27324)ˣ, (ℤ/27588)ˣ, (ℤ/28842)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C24×C3×C5×C11
socle, prime radicalC24×C3×C5×C11C3
LCSG ▷ C1
UCSC1 ◁ G

804 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C9×C11, C25×C5×C9×C11, C24×C5×C11×C27, …
maximal normal subgroup ofC23×C4×C5×C9×C11, C25×C5×C9×C11, C24×C5×C11×C27, …
maximal quotient ofC23×C4×C5×C9×C11, C25×C5×C9×C11, C24×C5×C11×C27, …
automorphism group ofC8×C11×C199, C8×C19×C121, C3×C8×C991, …
outer automorphism group ofC8×C11×C199, C8×C19×C121, C3×C8×C991, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.