Finite Group Databasebeta

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C23×C32×C4×C9×C11 #72205485

order28512
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5016453120
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C33

Aliases

abelianC23×C32×C4×C9×C11
multiplicative(ℤ/39767)ˣ, (ℤ/44555)ˣ, (ℤ/49647)ˣ, (ℤ/51129)ˣ, (ℤ/52059)ˣ, (ℤ/53613)ˣ, (ℤ/54327)ˣ, (ℤ/56511)ˣ, (ℤ/57285)ˣ, (ℤ/62685)ˣ, (ℤ/63315)ˣ, (ℤ/66196)ˣ, (ℤ/69412)ˣ, (ℤ/72436)ˣ, (ℤ/79534)ˣ, (ℤ/89110)ˣ, (ℤ/89244)ˣ, (ℤ/93132)ˣ, (ℤ/94068)ˣ, (ℤ/99294)ˣ, (ℤ/100044)ˣ, (ℤ/102258)ˣ, (ℤ/104118)ˣ, (ℤ/107226)ˣ, (ℤ/108654)ˣ, (ℤ/113022)ˣ, (ℤ/114570)ˣ, (ℤ/125370)ˣ, (ℤ/126630)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3C24×C33×C11
socle, prime radicalC24×C33×C11C2×C3
LCSG ▷ C1
UCSC1 ◁ G

11800 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

28512 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.