Finite Group Databasebeta

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C23×C33×C4×C11 #72188252

order9504
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2415329280
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C33

Aliases

abelianC23×C33×C4×C11
multiplicative(ℤ/18291)ˣ, (ℤ/18837)ˣ, (ℤ/21105)ˣ, (ℤ/24388)ˣ, (ℤ/31356)ˣ, (ℤ/36582)ˣ, (ℤ/37674)ˣ, (ℤ/42210)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C33×C11
socle, prime radicalC24×C33×C11C2
LCSG ▷ C1
UCSC1 ◁ G

6608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9504 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C33×C8×C11, C22×C33×C42×C11, C24×C33×C4×C11, …
maximal normal subgroup ofC23×C33×C8×C11, C22×C33×C42×C11, C24×C33×C4×C11, …
maximal quotient ofC23×C33×C8×C11, C22×C33×C42×C11, C24×C33×C4×C11, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.