Finite Group Databasebeta

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C23×C5×C13×C16 #72187241

order8320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4128768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C5×C13×C16
multiplicative(ℤ/17816)ˣ, (ℤ/25152)ˣ, (ℤ/26724)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C24×C5×C13
socle, prime radicalC24×C5×C13C8
LCSG ▷ C1
UCSC1 ◁ G

880 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C5×C13×C32, C24×C5×C13×C16, C22×C4×C5×C13×C16, …
maximal normal subgroup ofC23×C5×C13×C32, C24×C5×C13×C16, C22×C4×C5×C13×C16, …
maximal quotient ofC23×C5×C13×C32, C24×C5×C13×C16, C22×C4×C5×C13×C16, …
automorphism group ofC8×C17×C131, C3×C64×C131
outer automorphism group ofC8×C17×C131, C3×C64×C131

GAP

Past the SmallGroups library coverage — no SmallGroups id.