Finite Group Databasebeta

← Prev (#72194251) Next (#72194253) →

C22×C3×C42×C5×C17 #72194252

order16320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 18874368
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C4

Aliases

abelianC22×C3×C42×C5×C17
multiplicative(ℤ/40840)ˣ, (ℤ/41200)ˣ, (ℤ/49008)ˣ, (ℤ/61260)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C24×C3×C5×C17
socle, prime radicalC24×C3×C5×C17C22
LCSG ▷ C1
UCSC1 ◁ G

1992 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C5×C8×C17, C2×C3×C43×C5×C17, C23×C3×C42×C5×C17
maximal normal subgroup ofC22×C3×C4×C5×C8×C17, C2×C3×C43×C5×C17, C23×C3×C42×C5×C17
maximal quotient ofC22×C3×C4×C5×C8×C17, C2×C3×C43×C5×C17, C23×C3×C42×C5×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.