Finite Group Databasebeta

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C3×C5×C16×C27 #72185607

order6480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10368
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C5×C16×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8×C9C2×C32×C5
socle, prime radicalC2×C32×C5C8×C9
LCSG ▷ C1
UCSC1 ◁ G

140 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×C27×C32, C2×C3×C5×C16×C27, C3×C5×C16×C81, …
maximal normal subgroup ofC3×C5×C27×C32, C2×C3×C5×C16×C27, C3×C5×C16×C81, …
maximal quotient ofC3×C5×C27×C32, C2×C3×C5×C16×C27, C3×C5×C16×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.