Finite Group Databasebeta

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C2×C32×C5×C9×C13 #72189140

order10530
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1119744
homologyAbelianization (H1) = G · Schur multiplier (H2) = C33

Aliases

abelianC2×C32×C5×C9×C13

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C2×C33×C5×C13
socle, prime radicalC2×C33×C5×C13C3
LCSG ▷ C1
UCSC1 ◁ G

400 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 ofC32×C4×C5×C9×C13, C22×C32×C5×C9×C13, C2×C32×C5×C13×C27, …
maximal normal subgroup ofC32×C4×C5×C9×C13, C22×C32×C5×C9×C13, C2×C32×C5×C13×C27, …
maximal quotient ofC32×C4×C5×C9×C13, C22×C32×C5×C9×C13, C2×C32×C5×C13×C27, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.