Finite Group Databasebeta

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C22×C3×C5×C9×C19 #72188917

order10260
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 46656
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2×C3

Aliases

abelianC22×C3×C5×C9×C19
multiplicative(ℤ/10849)ˣ, (ℤ/11191)ˣ, (ℤ/15417)ˣ, (ℤ/21698)ˣ, (ℤ/22382)ˣ, (ℤ/30834)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3C22×C32×C5×C19
socle, prime radicalC22×C32×C5×C19C3
LCSG ▷ C1
UCSC1 ◁ G

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10260 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C5×C9×C19, C23×C3×C5×C9×C19, C22×C3×C5×C19×C27, …
maximal normal subgroup ofC2×C3×C4×C5×C9×C19, C23×C3×C5×C9×C19, C22×C3×C5×C19×C27, …
maximal quotient ofC2×C3×C4×C5×C9×C19, C23×C3×C5×C9×C19, C22×C3×C5×C19×C27, …
automorphism group ofC19×C571, C31×C361, C2×C27×C571
outer automorphism group ofC19×C571, C31×C361, C2×C27×C571

GAP

Past the SmallGroups library coverage — no SmallGroups id.