Finite Group Databasebeta

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C2×C3×C8×C64 #72182803

order3072
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 262144
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C8

Aliases

abelianC2×C3×C8×C64
multiplicative(ℤ/6176)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C32C23×C3
socle, prime radicalC23×C3C4×C32
LCSG ▷ C1
UCSC1 ◁ G

634 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3072 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C8×C128, C2×C3×C16×C64, C3×C4×C8×C64, …
maximal normal subgroup ofC2×C3×C8×C128, C2×C3×C16×C64, C3×C4×C8×C64, …
maximal quotient ofC2×C3×C8×C128, C2×C3×C16×C64, C3×C4×C8×C64, …
automorphism group ofC32×C193
outer automorphism group ofC32×C193

GAP

Past the SmallGroups library coverage — no SmallGroups id.