Finite Group Databasebeta

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C23×C3×C4×C9×C23 #72197528

order19872
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 51093504
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C3

Aliases

abelianC23×C3×C4×C9×C23
multiplicative(ℤ/31255)ˣ, (ℤ/34827)ˣ, (ℤ/36519)ˣ, (ℤ/39615)ˣ, (ℤ/40185)ˣ, (ℤ/41144)ˣ, (ℤ/42104)ˣ, (ℤ/42256)ˣ, (ℤ/44415)ˣ, (ℤ/46424)ˣ, (ℤ/46436)ˣ, (ℤ/48692)ˣ, (ℤ/52820)ˣ, (ℤ/59688)ˣ, (ℤ/59832)ˣ, (ℤ/60048)ˣ, (ℤ/61716)ˣ, (ℤ/62510)ˣ, (ℤ/62604)ˣ, (ℤ/63156)ˣ, (ℤ/65988)ˣ, (ℤ/69636)ˣ, (ℤ/69654)ˣ, (ℤ/73038)ˣ, (ℤ/75060)ˣ, (ℤ/79230)ˣ, (ℤ/80370)ˣ, (ℤ/88830)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C24×C32×C23
socle, prime radicalC24×C32×C23C2×C3
LCSG ▷ C1
UCSC1 ◁ G

2360 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

19872 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.