Finite Group Databasebeta

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C25×C32×C52 #72186282

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 230385254400
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3×C5

Aliases

abelianC25×C32×C52
multiplicative(ℤ/19096)ˣ, (ℤ/24552)ˣ, (ℤ/28644)ˣ

Subgroups

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

17952 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7200 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C32×C4×C52, C26×C32×C52, C25×C3×C52×C9, …
maximal normal subgroup ofC24×C32×C4×C52, C26×C32×C52, C25×C3×C52×C9, …
maximal quotient ofC24×C32×C4×C52, C26×C32×C52, C25×C3×C52×C9, …
automorphism group ofC7×C8×C11×C31, C8×C9×C11×C31
outer automorphism group ofC7×C8×C11×C31, C8×C9×C11×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.