Finite Group Databasebeta

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C22×C3×C16×C43 #72187188

order8256
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 64512
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C16×C43

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C23×C3×C43
socle, prime radicalC23×C3×C43C8
LCSG ▷ C1
UCSC1 ◁ G

196 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8256 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C32×C43, C2×C3×C4×C16×C43, C23×C3×C16×C43, …
maximal normal subgroup ofC22×C3×C32×C43, C2×C3×C4×C16×C43, C23×C3×C16×C43, …
maximal quotient ofC22×C3×C32×C43, C2×C3×C4×C16×C43, C23×C3×C16×C43, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.