Finite Group Databasebeta

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C3×C5×C16×C25 #72185193

order6000
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 32000
homologyAbelianization (H1) = G · Schur multiplier (H2) = C5

Aliases

abelianC3×C5×C16×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5×C8C2×C3×C52
socle, prime radicalC2×C3×C52C5×C8
LCSG ▷ C1
UCSC1 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6000 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C25×C32, C2×C3×C5×C16×C25, C5×C9×C16×C25, …
maximal normal subgroup ofC3×C5×C25×C32, C2×C3×C5×C16×C25, C5×C9×C16×C25, …
maximal quotient ofC3×C5×C25×C32, C2×C3×C5×C16×C25, C5×C9×C16×C25, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.