Finite Group Databasebeta

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C23×C5×C9×C25 #72187802

order9000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2016000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C5

Aliases

abelianC23×C5×C9×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C5C23×C3×C52
socle, prime radicalC23×C3×C52C3×C5
LCSG ▷ C1
UCSC1 ◁ G

672 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C5×C9×C25, C24×C5×C9×C25, C23×C5×C25×C27, …
maximal normal subgroup ofC22×C4×C5×C9×C25, C24×C5×C9×C25, C23×C5×C25×C27, …
maximal quotient ofC22×C4×C5×C9×C25, C24×C5×C9×C25, C23×C5×C25×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.