Finite Group Databasebeta

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C23×C3×C4×C9×C16 #72192031

order13824
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 19025362944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C3×C4

Aliases

abelianC23×C3×C4×C9×C16
multiplicative(ℤ/33592)ˣ, (ℤ/33915)ˣ, (ℤ/35224)ˣ, (ℤ/36176)ˣ, (ℤ/42560)ˣ, (ℤ/45220)ˣ, (ℤ/45288)ˣ, (ℤ/46512)ˣ, (ℤ/47424)ˣ, (ℤ/47736)ˣ, (ℤ/49728)ˣ, (ℤ/50388)ˣ, (ℤ/51408)ˣ, (ℤ/52836)ˣ, (ℤ/54720)ˣ, (ℤ/58140)ˣ, (ℤ/60480)ˣ, (ℤ/64260)ˣ, (ℤ/67830)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C8C25×C32
socle, prime radicalC25×C32C2×C3×C8
LCSG ▷ C1
UCSC1 ◁ G

31380 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13824 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C4×C9×C32, C23×C3×C8×C9×C16, C22×C3×C42×C9×C16, …
maximal normal subgroup ofC23×C3×C4×C9×C32, C23×C3×C8×C9×C16, C22×C3×C42×C9×C16, …
maximal quotient ofC23×C3×C4×C9×C32, C23×C3×C8×C9×C16, C22×C3×C42×C9×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.