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C23×C3×C9×C49 #72189173

order10584
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 762048
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C3

Aliases

abelianC23×C3×C9×C49
multiplicative(ℤ/18543)ˣ, (ℤ/19551)ˣ, (ℤ/24724)ˣ, (ℤ/26068)ˣ, (ℤ/31788)ˣ, (ℤ/37044)ˣ, (ℤ/37086)ˣ, (ℤ/39102)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC3×C7C23×C32×C7
socle, prime radicalC23×C32×C7C3×C7
LCSG ▷ C1
UCSC1 ◁ G

480 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10584 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C4×C9×C49, C24×C3×C9×C49, C23×C3×C27×C49, …
maximal normal subgroup ofC22×C3×C4×C9×C49, C24×C3×C9×C49, C23×C3×C27×C49, …
maximal quotient ofC22×C3×C4×C9×C49, C24×C3×C9×C49, C23×C3×C27×C49, …
automorphism group ofC3×C19×C343, C4×C19×C343
outer automorphism group ofC3×C19×C343, C4×C19×C343

GAP

Past the SmallGroups library coverage — no SmallGroups id.