Finite Group Databasebeta

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C2×C1024 #72182027

order2048
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2048
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C1024
multiplicative(ℤ/4096)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC512C22
socle, prime radicalC22C512
LCSG ▷ C1
UCSC1 ◁ G
LECSG ▷ C512 ▷ C256 ▷ C128 ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2048 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C2048, C4×C1024, C22×C1024, …
maximal normal subgroup ofC2×C2048, C4×C1024, C22×C1024, …
maximal quotient ofC2×C2048, C4×C1024, C22×C1024, …
automorphism group ofC4096
outer automorphism group ofC4096

GAP

Past the SmallGroups library coverage — no SmallGroups id.