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C2×C3×C16×C64 #72185306

order6144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2097152
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C16

Aliases

abelianC2×C3×C16×C64
multiplicative(ℤ/9843)ˣ, (ℤ/12352)ˣ, (ℤ/13124)ˣ, (ℤ/19686)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C32C23×C3
socle, prime radicalC23×C3C8×C32
LCSG ▷ C1
UCSC1 ◁ G

1136 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6144 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C16×C128, C3×C4×C16×C64, C22×C3×C16×C64, …
maximal normal subgroup ofC2×C3×C16×C128, C3×C4×C16×C64, C22×C3×C16×C64, …
maximal quotient ofC2×C3×C16×C128, C3×C4×C16×C64, C22×C3×C16×C64, …
automorphism group ofC3×C17×C193, C64×C193
outer automorphism group ofC3×C17×C193, C64×C193

GAP

Past the SmallGroups library coverage — no SmallGroups id.