Finite Group Databasebeta

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C24×C4×C5×C9×C11 #72208430

order31680
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2477260800
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C4×C5×C9×C11
multiplicative(ℤ/72105)ˣ, (ℤ/74888)ˣ, (ℤ/76912)ˣ, (ℤ/87400)ˣ, (ℤ/87560)ˣ, (ℤ/91960)ˣ, (ℤ/96140)ˣ, (ℤ/99912)ˣ, (ℤ/104808)ˣ, (ℤ/105072)ˣ, (ℤ/107448)ˣ, (ℤ/109296)ˣ, (ℤ/110352)ˣ, (ℤ/112332)ˣ, (ℤ/118920)ˣ, (ℤ/119400)ˣ, (ℤ/124200)ˣ, (ℤ/130680)ˣ, (ℤ/131100)ˣ, (ℤ/131340)ˣ, (ℤ/136620)ˣ, (ℤ/137940)ˣ, (ℤ/144210)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C25×C3×C5×C11
socle, prime radicalC25×C3×C5×C11C2×C3
LCSG ▷ C1
UCSC1 ◁ G

8172 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

31680 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.