Finite Group Databasebeta

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C23×C17×C25 #72183072

order3400
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 53760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC23×C17×C25

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC5C23×C5×C17
socle, prime radicalC23×C5×C17C5
LCSG ▷ C1
UCSC1 ◁ G

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3400 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C17×C25, C24×C17×C25, C23×C3×C17×C25, …
maximal normal subgroup ofC22×C4×C17×C25, C24×C17×C25, C23×C3×C17×C25, …
maximal quotient ofC22×C4×C17×C25, C24×C17×C25, C23×C3×C17×C25, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.