Finite Group Databasebeta

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C3×C5×C23×C27 #72188113

order9315
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 28512
homologyAbelianization (H1) = G · Schur multiplier (H2) = C3

Aliases

abelianC3×C5×C23×C27

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C32×C5×C23
socle, prime radicalC32×C5×C23C9
LCSG ▷ C1
UCSC1 ◁ G

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9315 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C23×C27, C3×C5×C23×C81, C5×C9×C23×C27, …
maximal normal subgroup ofC2×C3×C5×C23×C27, C3×C5×C23×C81, C5×C9×C23×C27, …
maximal quotient ofC2×C3×C5×C23×C27, C3×C5×C23×C81, C5×C9×C23×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.