Finite Group Databasebeta

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C22×C3×C43×C8 #72185339

order6144
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1108307720798208
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C46

Aliases

abelianC22×C3×C43×C8

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23×C4C26×C3
socle, prime radicalC26×C3C23×C4
LCSG ▷ C1
UCSC1 ◁ G

410064 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×C43×C16, C22×C3×C42×C82, C2×C3×C44×C8, …
maximal normal subgroup ofC22×C3×C43×C16, C22×C3×C42×C82, C2×C3×C44×C8, …
maximal quotient ofC22×C3×C43×C16, C22×C3×C42×C82, C2×C3×C44×C8, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.