Finite Group Databasebeta

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C2×C3×C5×C13×C27 #72189138

order10530
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 15552
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC2×C3×C5×C13×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C2×C32×C5×C13
socle, prime radicalC2×C32×C5×C13C9
LCSG ▷ C1
UCSC1 ◁ G

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10530 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C5×C13×C27, C22×C3×C5×C13×C27, C2×C3×C5×C13×C81, …
maximal normal subgroup ofC3×C4×C5×C13×C27, C22×C3×C5×C13×C27, C2×C3×C5×C13×C81, …
maximal quotient ofC3×C4×C5×C13×C27, C22×C3×C5×C13×C27, C2×C3×C5×C13×C81, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.