Finite Group Databasebeta

← Prev (#72190490) Next (#72190492) →

C22×C33×C42×C7 #72190491

order12096
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 9937354752
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C33×C4

Aliases

abelianC22×C33×C42×C7
multiplicative(ℤ/19565)ˣ, (ℤ/23751)ˣ, (ℤ/25155)ˣ, (ℤ/28665)ˣ, (ℤ/39130)ˣ, (ℤ/47502)ˣ, (ℤ/50310)ˣ, (ℤ/57330)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C33×C7
socle, prime radicalC24×C33×C7C22
LCSG ▷ C1
UCSC1 ◁ G

13944 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 ofC22×C33×C4×C7×C8, C2×C33×C43×C7, C23×C33×C42×C7
maximal normal subgroup ofC22×C33×C4×C7×C8, C2×C33×C43×C7, C23×C33×C42×C7
maximal quotient ofC22×C33×C4×C7×C8, C2×C33×C43×C7, C23×C33×C42×C7

GAP

Past the SmallGroups library coverage — no SmallGroups id.