Finite Group Databasebeta

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C22×C3×C4×C7×C8×C11 #72206448

order29568
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 23592960
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C3×C4×C7×C8×C11
multiplicative(ℤ/54201)ˣ, (ℤ/57405)ˣ, (ℤ/61232)ˣ, (ℤ/62176)ˣ, (ℤ/64168)ˣ, (ℤ/64785)ˣ, (ℤ/65415)ˣ, (ℤ/69104)ˣ, (ℤ/69776)ˣ, (ℤ/72268)ˣ, (ℤ/74080)ˣ, (ℤ/76540)ˣ, (ℤ/86380)ˣ, (ℤ/87220)ˣ, (ℤ/88848)ˣ, (ℤ/92916)ˣ, (ℤ/96252)ˣ, (ℤ/108402)ˣ, (ℤ/111060)ˣ, (ℤ/114810)ˣ, (ℤ/129570)ˣ, (ℤ/130830)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C24×C3×C7×C11
socle, prime radicalC24×C3×C7×C11C2×C4
LCSG ▷ C1
UCSC1 ◁ G

3040 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

29568 conjugacy classes. The character table is too large to display.

GAP

Past the SmallGroups library coverage — no SmallGroups id.