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C22×C3×C16×C64 #72190646

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 201326592
homologyAbelianization (H1) = G · Schur multiplier (H2) = C25×C16

Aliases

abelianC22×C3×C16×C64
multiplicative(ℤ/26248)ˣ, (ℤ/30464)ˣ, (ℤ/37056)ˣ, (ℤ/39168)ˣ, (ℤ/39372)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C32C24×C3
socle, prime radicalC24×C3C8×C32
LCSG ▷ C1
UCSC1 ◁ G

5590 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C16×C128, C22×C3×C32×C64, C2×C3×C4×C16×C64, …
maximal normal subgroup ofC22×C3×C16×C128, C22×C3×C32×C64, C2×C3×C4×C16×C64, …
maximal quotient ofC22×C3×C16×C128, C22×C3×C32×C64, C2×C3×C4×C16×C64, …
automorphism group ofC8×C17×C193, C7×C17×C256
outer automorphism group ofC8×C17×C193, C7×C17×C256

GAP

Past the SmallGroups library coverage — no SmallGroups id.