Finite Group Databasebeta

← Prev (#72193363) Next (#72193365) →

C3×C43×C5×C16 #72193364

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 22548578304
homologyAbelianization (H1) = G · Schur multiplier (H2) = C46

Aliases

abelianC3×C43×C5×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C8C24×C3×C5
socle, prime radicalC24×C3×C5C23×C8
LCSG ▷ C1
UCSC1 ◁ G

18708 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C43×C5×C32, C3×C42×C5×C8×C16, C2×C3×C43×C5×C16
maximal normal subgroup ofC3×C43×C5×C32, C3×C42×C5×C8×C16, C2×C3×C43×C5×C16
maximal quotient ofC3×C43×C5×C32, C3×C42×C5×C8×C16, C2×C3×C43×C5×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.