Finite Group Databasebeta

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C22×C4×C16×C64 #72194346

order16384
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 824633720832
homologyAbelianization (H1) = G · Schur multiplier (H2) = C27×C42×C16

Aliases

abelianC22×C4×C16×C64
multiplicative(ℤ/65280)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8×C32C25
socle, prime radicalC25C2×C8×C32
LCSG ▷ C1
UCSC1 ◁ G
LECSG ▷ C2×C8×C32 ▷ C4×C16 ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1

57345 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16384 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C4×C16×C128, C22×C4×C32×C64, C22×C8×C16×C64, …
maximal normal subgroup ofC22×C4×C16×C128, C22×C4×C32×C64, C22×C8×C16×C64, …
maximal quotient ofC22×C4×C16×C128, C22×C4×C32×C64, C22×C8×C16×C64, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.