Finite Group Databasebeta

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C22×C3×C8×C81 #72186709

order7776
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 373248
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC22×C3×C8×C81

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C27C23×C32
socle, prime radicalC23×C32C4×C27
LCSG ▷ C1
UCSC1 ◁ G

684 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

7776 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C16×C81, C2×C3×C4×C8×C81, C23×C3×C8×C81, …
maximal normal subgroup ofC22×C3×C16×C81, C2×C3×C4×C8×C81, C23×C3×C8×C81, …
maximal quotient ofC22×C3×C16×C81, C2×C3×C4×C8×C81, C23×C3×C8×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.