Finite Group Databasebeta

← Prev (#72189955) Next (#72189957) →

C24×C32×C5×C16 #72189956

order11520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 7927234560
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210×C3

Aliases

abelianC24×C32×C5×C16
multiplicative(ℤ/29512)ˣ, (ℤ/37944)ˣ, (ℤ/40488)ˣ, (ℤ/41664)ˣ, (ℤ/44268)ˣ, (ℤ/44352)ˣ, (ℤ/47124)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C25×C32×C5
socle, prime radicalC25×C32×C5C8
LCSG ▷ C1
UCSC1 ◁ G

15540 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C32×C5×C32, C23×C32×C4×C5×C16, C25×C32×C5×C16
maximal normal subgroup ofC24×C32×C5×C32, C23×C32×C4×C5×C16, C25×C32×C5×C16
maximal quotient ofC24×C32×C5×C32, C23×C32×C4×C5×C16, C25×C32×C5×C16
automorphism group ofC7×C8×C17×C31
outer automorphism group ofC7×C8×C17×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.