Finite Group Databasebeta

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C24×C5×C125 #72188683

order10000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 201600000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C5

Aliases

abelianC24×C5×C125
multiplicative(ℤ/22088)ˣ, (ℤ/33132)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC25C24×C52
socle, prime radicalC24×C52C25
LCSG ▷ C1
UCSC1 ◁ G

1340 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C5×C125, C25×C5×C125, C24×C3×C5×C125
maximal normal subgroup ofC23×C4×C5×C125, C25×C5×C125, C24×C3×C5×C125
maximal quotient ofC23×C4×C5×C125, C25×C5×C125, C24×C3×C5×C125
automorphism group ofC8×C11×C251
outer automorphism group ofC8×C11×C251

GAP

Past the SmallGroups library coverage — no SmallGroups id.