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C22×C3×C4×C5×C8×C9 #72195164

order17280
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 84934656
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C3×C4

Aliases

abelianC22×C3×C4×C5×C8×C9
multiplicative(ℤ/27265)ˣ, (ℤ/28105)ˣ, (ℤ/30381)ˣ, (ℤ/31317)ˣ, (ℤ/31857)ˣ, (ℤ/33945)ˣ, (ℤ/35055)ˣ, (ℤ/35624)ˣ, (ℤ/36135)ˣ, (ℤ/36208)ˣ, (ℤ/36704)ˣ, (ℤ/37088)ˣ, (ℤ/38325)ˣ, (ℤ/38745)ˣ, (ℤ/40508)ˣ, (ℤ/40544)ˣ, (ℤ/41756)ˣ, (ℤ/42476)ˣ, (ℤ/45260)ˣ, (ℤ/51100)ˣ, (ℤ/52128)ˣ, (ℤ/52704)ˣ, (ℤ/53436)ˣ, (ℤ/54530)ˣ, (ℤ/54612)ˣ, (ℤ/56210)ˣ, (ℤ/57564)ˣ, (ℤ/60762)ˣ, (ℤ/62634)ˣ, (ℤ/63714)ˣ, (ℤ/65700)ˣ, (ℤ/67890)ˣ, (ℤ/70110)ˣ, (ℤ/72270)ˣ, (ℤ/76650)ˣ, (ℤ/77490)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4C24×C32×C5
socle, prime radicalC24×C32×C5C2×C3×C4
LCSG ▷ C1
UCSC1 ◁ G

7600 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

17280 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.