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C22×C32×C42×C5×C9 #72203103

order25920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 13759414272
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C33×C4

Aliases

abelianC22×C32×C42×C5×C9
multiplicative(ℤ/37037)ˣ, (ℤ/38285)ˣ, (ℤ/40145)ˣ, (ℤ/40565)ˣ, (ℤ/43225)ˣ, (ℤ/44733)ˣ, (ℤ/45201)ˣ, (ℤ/47397)ˣ, (ℤ/47619)ˣ, (ℤ/49413)ˣ, (ℤ/51615)ˣ, (ℤ/52155)ˣ, (ℤ/54405)ˣ, (ℤ/55575)ˣ, (ℤ/57015)ˣ, (ℤ/57645)ˣ, (ℤ/58275)ˣ, (ℤ/59644)ˣ, (ℤ/60268)ˣ, (ℤ/61425)ˣ, (ℤ/63196)ˣ, (ℤ/65884)ˣ, (ℤ/74074)ˣ, (ℤ/76570)ˣ, (ℤ/80290)ˣ, (ℤ/81130)ˣ, (ℤ/81252)ˣ, (ℤ/84708)ˣ, (ℤ/85644)ˣ, (ℤ/86450)ˣ, (ℤ/89466)ˣ, (ℤ/90402)ˣ, (ℤ/94794)ˣ, (ℤ/95238)ˣ, (ℤ/98826)ˣ, (ℤ/103230)ˣ, (ℤ/104310)ˣ, (ℤ/108810)ˣ, (ℤ/111150)ˣ, (ℤ/114030)ˣ, (ℤ/115290)ˣ, (ℤ/116550)ˣ, (ℤ/122850)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C3C24×C33×C5
socle, prime radicalC24×C33×C5C22×C3
LCSG ▷ C1
UCSC1 ◁ G

24900 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

25920 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.