Finite Group Databasebeta

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C24×C32×C52 #72183275

order3600
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 464486400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3×C5

Aliases

abelianC24×C32×C52
multiplicative(ℤ/7161)ˣ, (ℤ/9548)ˣ, (ℤ/12276)ˣ, (ℤ/14322)ˣ

Subgroups

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

3216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3600 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C32×C4×C52, C25×C32×C52, C24×C3×C52×C9, …
maximal normal subgroup ofC23×C32×C4×C52, C25×C32×C52, C24×C3×C52×C9, …
maximal quotient ofC23×C32×C4×C52, C25×C32×C52, C24×C3×C52×C9, …
automorphism group ofC3×C7×C11×C31, C4×C7×C11×C31
outer automorphism group ofC3×C7×C11×C31, C4×C7×C11×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.