Finite Group Databasebeta

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C23×C32×C4×C5×C17 #72201753

order24480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 66060288
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C32×C4×C5×C17
multiplicative(ℤ/39655)ˣ, (ℤ/44187)ˣ, (ℤ/47895)ˣ, (ℤ/50264)ˣ, (ℤ/50985)ˣ, (ℤ/51088)ˣ, (ℤ/54075)ˣ, (ℤ/57176)ˣ, (ℤ/58916)ˣ, (ℤ/63860)ˣ, (ℤ/72100)ˣ, (ℤ/73512)ˣ, (ℤ/75396)ˣ, (ℤ/79310)ˣ, (ℤ/85764)ˣ, (ℤ/88374)ˣ, (ℤ/92700)ˣ, (ℤ/95790)ˣ, (ℤ/101970)ˣ, (ℤ/108150)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C32×C5×C17
socle, prime radicalC24×C32×C5×C17C2
LCSG ▷ C1
UCSC1 ◁ G

2832 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24480 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.