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C23×C3×C13×C32 #72188643

order9984
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4128768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C13×C32
multiplicative(ℤ/29976)ˣ, (ℤ/30336)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC16C24×C3×C13
socle, prime radicalC24×C3×C13C16
LCSG ▷ C1
UCSC1 ◁ G

1084 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9984 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C13×C64, C24×C3×C13×C32, C22×C3×C4×C13×C32, …
maximal normal subgroup ofC23×C3×C13×C64, C24×C3×C13×C32, C22×C3×C4×C13×C32, …
maximal quotient ofC23×C3×C13×C64, C24×C3×C13×C32, C22×C3×C4×C13×C32, …
automorphism group ofC3×C8×C1249, C3×C79×C128
outer automorphism group ofC3×C8×C1249, C3×C79×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.