Finite Group Databasebeta

← Prev (#72182102) Next (#72182104) →

C2×C5×C13×C16 #72182103

order2080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1536
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C5×C13×C16
multiplicative(ℤ/2227)ˣ, (ℤ/4454)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C22×C5×C13
socle, prime radicalC22×C5×C13C8
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C13×C32, C4×C5×C13×C16, C22×C5×C13×C16, …
maximal normal subgroup ofC2×C5×C13×C32, C4×C5×C13×C16, C22×C5×C13×C16, …
maximal quotient ofC2×C5×C13×C32, C4×C5×C13×C16, C22×C5×C13×C16, …
automorphism group ofC17×C131, C2×C17×C131
outer automorphism group ofC17×C131, C2×C17×C131

GAP

Past the SmallGroups library coverage — no SmallGroups id.