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C24×C3×C4×C5×C13 #72190828

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 990904320
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C3×C4×C5×C13
multiplicative(ℤ/32648)ˣ, (ℤ/34760)ˣ, (ℤ/36680)ˣ, (ℤ/39432)ˣ, (ℤ/40872)ˣ, (ℤ/41448)ˣ, (ℤ/41712)ˣ, (ℤ/41976)ˣ, (ℤ/44016)ˣ, (ℤ/44616)ˣ, (ℤ/47160)ˣ, (ℤ/47400)ˣ, (ℤ/48972)ˣ, (ℤ/52140)ˣ, (ℤ/55020)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C25×C3×C5×C13
socle, prime radicalC25×C3×C5×C13C2
LCSG ▷ C1
UCSC1 ◁ G

5448 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C5×C8×C13, C23×C3×C42×C5×C13, C25×C3×C4×C5×C13
maximal normal subgroup ofC24×C3×C5×C8×C13, C23×C3×C42×C5×C13, C25×C3×C4×C5×C13
maximal quotient ofC24×C3×C5×C8×C13, C23×C3×C42×C5×C13, C25×C3×C4×C5×C13
automorphism group ofC7×C8×C11×C53
outer automorphism group ofC7×C8×C11×C53

GAP

Past the SmallGroups library coverage — no SmallGroups id.