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C2×C4096 #72187041

order8192
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8192
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C4096
multiplicative(ℤ/16384)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2048C22
socle, prime radicalC22C2048
LCSG ▷ C1
UCSC1 ◁ G
LECSG ▷ C2048 ▷ C1024 ▷ C512 ▷ C256 ▷ C128 ▷ C64 ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1

38 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8192 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C8192, C4×C4096, C22×C4096, …
maximal normal subgroup ofC2×C8192, C4×C4096, C22×C4096, …
maximal quotient ofC2×C8192, C4×C4096, C22×C4096, …
automorphism group ofC16384
outer automorphism group ofC16384

GAP

Past the SmallGroups library coverage — no SmallGroups id.