Finite Group Databasebeta

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C32×C4×C8×C27 #72186705

order7776
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 8957952
homologyAbelianization (H1) = G · Schur multiplier (H2) = C33×C4

Aliases

abelianC32×C4×C8×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4×C9C22×C33
socle, prime radicalC22×C33C2×C4×C9
LCSG ▷ C1
UCSC1 ◁ G

1584 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 ofC32×C4×C16×C27, C32×C82×C27, C2×C32×C4×C8×C27, …
maximal normal subgroup ofC32×C4×C16×C27, C32×C82×C27, C2×C32×C4×C8×C27, …
maximal quotient ofC32×C4×C16×C27, C32×C82×C27, C2×C32×C4×C8×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.