Finite Group Databasebeta

← Prev (#72194245) Next (#72194247) →

C3×C4×C5×C16×C17 #72194246

order16320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 32768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC3×C4×C5×C16×C17
multiplicative(ℤ/17357)ˣ, (ℤ/17629)ˣ, (ℤ/17693)ˣ, (ℤ/34714)ˣ, (ℤ/35258)ˣ, (ℤ/35386)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C22×C3×C5×C17
socle, prime radicalC22×C3×C5×C17C2×C8
LCSG ▷ C1
UCSC1 ◁ G

232 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 ofC3×C4×C5×C17×C32, C3×C5×C8×C16×C17, C2×C3×C4×C5×C16×C17
maximal normal subgroup ofC3×C4×C5×C17×C32, C3×C5×C8×C16×C17, C2×C3×C4×C5×C16×C17
maximal quotient ofC3×C4×C5×C17×C32, C3×C5×C8×C16×C17, C2×C3×C4×C5×C16×C17
automorphism group ofC17×C1021, C13×C1361
outer automorphism group ofC17×C1021, C13×C1361

GAP

Past the SmallGroups library coverage — no SmallGroups id.