Finite Group Databasebeta

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C24×C32×C5×C13 #72188145

order9360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 46448640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC24×C32×C5×C13
multiplicative(ℤ/18249)ˣ, (ℤ/19592)ˣ, (ℤ/24332)ˣ, (ℤ/29388)ˣ, (ℤ/31284)ˣ, (ℤ/33012)ˣ, (ℤ/36498)ˣ

Subgroups

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

1608 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C32×C4×C5×C13, C25×C32×C5×C13, C24×C3×C5×C9×C13, …
maximal normal subgroup ofC23×C32×C4×C5×C13, C25×C32×C5×C13, C24×C3×C5×C9×C13, …
maximal quotient ofC23×C32×C4×C5×C13, C25×C32×C5×C13, C24×C3×C5×C9×C13, …
automorphism group ofC8×C31×C79
outer automorphism group ofC8×C31×C79

GAP

Past the SmallGroups library coverage — no SmallGroups id.