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C23×C5×C128 #72184451

order5120
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2752512
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C5×C128
multiplicative(ℤ/15384)ˣ, (ℤ/16896)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC64C24×C5
socle, prime radicalC24×C5C64
LCSG ▷ C1
UCSC1 ◁ G

746 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5120 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C5×C256, C24×C5×C128, C22×C4×C5×C128, …
maximal normal subgroup ofC23×C5×C256, C24×C5×C128, C22×C4×C5×C128, …
maximal quotient ofC23×C5×C256, C24×C5×C128, C22×C4×C5×C128, …
automorphism group ofC3×C8×C641, C3×C11×C512
outer automorphism group ofC3×C8×C641, C3×C11×C512

GAP

Past the SmallGroups library coverage — no SmallGroups id.