Finite Group Databasebeta

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C24×C3×C4×C5×C17 #72194253

order16320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1321205760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C3×C4×C5×C17
multiplicative(ℤ/45320)ˣ, (ℤ/54384)ˣ, (ℤ/61800)ˣ, (ℤ/67980)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C3×C5×C17
socle, prime radicalC25×C3×C5×C17C2
LCSG ▷ C1
UCSC1 ◁ G

5448 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C5×C8×C17, C23×C3×C42×C5×C17, C25×C3×C4×C5×C17
maximal normal subgroup ofC24×C3×C5×C8×C17, C23×C3×C42×C5×C17, C25×C3×C4×C5×C17
maximal quotient ofC24×C3×C5×C8×C17, C23×C3×C42×C5×C17, C25×C3×C4×C5×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.