Finite Group Databasebeta

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C25×C32×C25 #72186281

order7200
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9599385600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3

Aliases

abelianC25×C32×C25
multiplicative(ℤ/25368)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C25×C32×C5
socle, prime radicalC25×C32×C5C5
LCSG ▷ C1
UCSC1 ◁ G

6732 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×C25, C26×C32×C25, C25×C3×C9×C25, …
maximal normal subgroup ofC24×C32×C4×C25, C26×C32×C25, C25×C3×C9×C25, …
maximal quotient ofC24×C32×C4×C25, C26×C32×C25, C25×C3×C9×C25, …
automorphism group ofC3×C7×C8×C151
outer automorphism group ofC3×C7×C8×C151

GAP

Past the SmallGroups library coverage — no SmallGroups id.