Finite Group Databasebeta

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C23×C32×C4×C5×C16 #72200381

order23040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 33822867456
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C3×C4

Aliases

abelianC23×C32×C4×C5×C16
multiplicative(ℤ/51051)ˣ, (ℤ/54808)ˣ, (ℤ/55335)ˣ, (ℤ/58072)ˣ, (ℤ/58905)ˣ, (ℤ/59024)ˣ, (ℤ/64064)ˣ, (ℤ/67480)ˣ, (ℤ/68068)ˣ, (ℤ/69440)ˣ, (ℤ/73780)ˣ, (ℤ/74664)ˣ, (ℤ/75192)ˣ, (ℤ/75888)ˣ, (ℤ/77376)ˣ, (ℤ/80976)ˣ, (ℤ/81984)ˣ, (ℤ/82212)ˣ, (ℤ/82368)ˣ, (ℤ/86760)ˣ, (ℤ/87108)ˣ, (ℤ/87516)ˣ, (ℤ/89280)ˣ, (ℤ/94860)ˣ, (ℤ/100800)ˣ, (ℤ/101220)ˣ, (ℤ/102102)ˣ, (ℤ/107100)ˣ, (ℤ/110670)ˣ, (ℤ/117810)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C25×C32×C5
socle, prime radicalC25×C32×C5C2×C8
LCSG ▷ C1
UCSC1 ◁ G

37656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

23040 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.