Finite Group Databasebeta

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C23×C3×C5×C128 #72193347

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5505024
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C5×C128
multiplicative(ℤ/35896)ˣ, (ℤ/39424)ˣ, (ℤ/46152)ˣ, (ℤ/47616)ˣ, (ℤ/50688)ˣ, (ℤ/53844)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC64C24×C3×C5
socle, prime radicalC24×C3×C5C64
LCSG ▷ C1
UCSC1 ◁ G

1492 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 ofC23×C3×C5×C256, C24×C3×C5×C128, C22×C3×C4×C5×C128
maximal normal subgroup ofC23×C3×C5×C256, C24×C3×C5×C128, C22×C3×C4×C5×C128
maximal quotient ofC23×C3×C5×C256, C24×C3×C5×C128, C22×C3×C4×C5×C128

GAP

Past the SmallGroups library coverage — no SmallGroups id.