Finite Group Databasebeta

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C23×C33×C4×C5 #72183865

order4320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 966131712
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C33

Aliases

abelianC23×C33×C4×C5
multiplicative(ℤ/8463)ˣ, (ℤ/9009)ˣ, (ℤ/9765)ˣ, (ℤ/11284)ˣ, (ℤ/14508)ˣ, (ℤ/15372)ˣ, (ℤ/16926)ˣ, (ℤ/18018)ˣ, (ℤ/19530)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C33×C5
socle, prime radicalC24×C33×C5C2
LCSG ▷ C1
UCSC1 ◁ G

6608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C33×C5×C8, C22×C33×C42×C5, C24×C33×C4×C5, …
maximal normal subgroup ofC23×C33×C5×C8, C22×C33×C42×C5, C24×C33×C4×C5, …
maximal quotient ofC23×C33×C5×C8, C22×C33×C42×C5, C24×C33×C4×C5, …
automorphism group ofC3×C7×C13×C31, C7×C9×C11×C13, C5×C7×C9×C31
outer automorphism group ofC3×C7×C13×C31, C7×C9×C11×C13, C5×C7×C9×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.