Finite Group Databasebeta

← Prev (#72190480) Next (#72190482) →

C2×C3×C4×C7×C8×C9 #72190481

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1327104
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C3×C4

Aliases

abelianC2×C3×C4×C7×C8×C9
multiplicative(ℤ/14819)ˣ, (ℤ/15695)ˣ, (ℤ/17885)ˣ, (ℤ/19053)ˣ, (ℤ/29638)ˣ, (ℤ/31390)ˣ, (ℤ/35770)ˣ, (ℤ/38106)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C3×C4C23×C32×C7
socle, prime radicalC23×C32×C7C2×C3×C4
LCSG ▷ C1
UCSC1 ◁ G

1620 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12096 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C7×C9×C16, C2×C3×C7×C82×C9, C3×C42×C7×C8×C9, …
maximal normal subgroup ofC2×C3×C4×C7×C9×C16, C2×C3×C7×C82×C9, C3×C42×C7×C8×C9, …
maximal quotient ofC2×C3×C4×C7×C9×C16, C2×C3×C7×C82×C9, C3×C42×C7×C8×C9, …
automorphism group ofC5×C43×C73
outer automorphism group ofC5×C43×C73

GAP

Past the SmallGroups library coverage — no SmallGroups id.