Finite Group Databasebeta

← Prev (#72201472) Next (#72201474) →

C23×C3×C7×C9×C16 #72201473

order24192
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 55738368
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C3×C7×C9×C16
multiplicative(ℤ/41667)ˣ, (ℤ/45087)ˣ, (ℤ/45339)ˣ, (ℤ/47481)ˣ, (ℤ/51224)ˣ, (ℤ/52288)ˣ, (ℤ/55556)ˣ, (ℤ/56504)ˣ, (ℤ/56896)ˣ, (ℤ/59584)ˣ, (ℤ/60116)ˣ, (ℤ/60452)ˣ, (ℤ/63308)ˣ, (ℤ/72648)ˣ, (ℤ/72792)ˣ, (ℤ/73152)ˣ, (ℤ/74304)ˣ, (ℤ/76836)ˣ, (ℤ/77292)ˣ, (ℤ/77724)ˣ, (ℤ/78948)ˣ, (ℤ/83334)ˣ, (ℤ/84672)ˣ, (ℤ/84756)ˣ, (ℤ/85428)ˣ, (ℤ/89964)ˣ, (ℤ/90174)ˣ, (ℤ/90678)ˣ, (ℤ/94962)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C8C24×C32×C7
socle, prime radicalC24×C32×C7C3×C8
LCSG ▷ C1
UCSC1 ◁ G

4400 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24192 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.