Finite Group Databasebeta

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C22×C3×C512 #72185296

order6144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49152
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C512
multiplicative(ℤ/14336)ˣ, (ℤ/18432)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC256C23×C3
socle, prime radicalC23×C3C256
LCSG ▷ C1
UCSC1 ◁ G

208 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 ofC22×C3×C1024, C23×C3×C512, C2×C3×C4×C512, …
maximal normal subgroup ofC22×C3×C1024, C23×C3×C512, C2×C3×C4×C512, …
maximal quotient ofC22×C3×C1024, C23×C3×C512, C2×C3×C4×C512, …
automorphism group ofC7×C2048, C9×C2048
outer automorphism group ofC7×C2048, C9×C2048

GAP

Past the SmallGroups library coverage — no SmallGroups id.