Finite Group Databasebeta

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C23×C3×C4×C11×C23 #72201562

order24288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9461760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C4×C11×C23
multiplicative(ℤ/37835)ˣ, (ℤ/42159)ˣ, (ℤ/47235)ˣ, (ℤ/47955)ˣ, (ℤ/48645)ˣ, (ℤ/50384)ˣ, (ℤ/50968)ˣ, (ℤ/51152)ˣ, (ℤ/55016)ˣ, (ℤ/55545)ˣ, (ℤ/56212)ˣ, (ℤ/56728)ˣ, (ℤ/59248)ˣ, (ℤ/62980)ˣ, (ℤ/63940)ˣ, (ℤ/72888)ˣ, (ℤ/72936)ˣ, (ℤ/74060)ˣ, (ℤ/75670)ˣ, (ℤ/76176)ˣ, (ℤ/76452)ˣ, (ℤ/82524)ˣ, (ℤ/84318)ˣ, (ℤ/85092)ˣ, (ℤ/94470)ˣ, (ℤ/95220)ˣ, (ℤ/95910)ˣ, (ℤ/97290)ˣ, (ℤ/111090)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C24×C3×C11×C23
socle, prime radicalC24×C3×C11×C23C2
LCSG ▷ C1
UCSC1 ◁ G

944 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

24288 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.