Finite Group Databasebeta

← Prev (#72189585) Next (#72189587) →

C2×C3×C42×C5×C23 #72189586

order11040
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 270336
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C5×C23
multiplicative(ℤ/14335)ˣ, (ℤ/15235)ˣ, (ℤ/15275)ˣ, (ℤ/16135)ˣ, (ℤ/17979)ˣ, (ℤ/20715)ˣ, (ℤ/20745)ˣ, (ℤ/20775)ˣ, (ℤ/22096)ˣ, (ℤ/23972)ˣ, (ℤ/27620)ˣ, (ℤ/27700)ˣ, (ℤ/28670)ˣ, (ℤ/30470)ˣ, (ℤ/30550)ˣ, (ℤ/32270)ˣ, (ℤ/35958)ˣ, (ℤ/41430)ˣ, (ℤ/41490)ˣ, (ℤ/41550)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C5×C23
socle, prime radicalC23×C3×C5×C23C22
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11040 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C5×C8×C23, C3×C43×C5×C23, C22×C3×C42×C5×C23
maximal normal subgroup ofC2×C3×C4×C5×C8×C23, C3×C43×C5×C23, C22×C3×C42×C5×C23
maximal quotient ofC2×C3×C4×C5×C8×C23, C3×C43×C5×C23, C22×C3×C42×C5×C23

GAP

Past the SmallGroups library coverage — no SmallGroups id.