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C22×C3×C4×C13×C17 #72189186

order10608
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 73728
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23

Aliases

abelianC22×C3×C4×C13×C17
multiplicative(ℤ/15505)ˣ, (ℤ/16377)ˣ, (ℤ/17277)ˣ, (ℤ/19905)ˣ, (ℤ/19935)ˣ, (ℤ/21232)ˣ, (ℤ/21836)ˣ, (ℤ/23036)ˣ, (ℤ/26540)ˣ, (ℤ/31010)ˣ, (ℤ/32754)ˣ, (ℤ/34554)ˣ, (ℤ/39810)ˣ, (ℤ/39870)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C23×C3×C13×C17
socle, prime radicalC23×C3×C13×C17C2
LCSG ▷ C1
UCSC1 ◁ G

216 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10608 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC22×C3×C8×C13×C17, C2×C3×C42×C13×C17, C23×C3×C4×C13×C17, …
maximal normal subgroup ofC22×C3×C8×C13×C17, C2×C3×C42×C13×C17, C23×C3×C4×C13×C17, …
maximal quotient ofC22×C3×C8×C13×C17, C2×C3×C42×C13×C17, C23×C3×C4×C13×C17, …
automorphism group ofC5×C7×C443
outer automorphism group ofC5×C7×C443

GAP

Past the SmallGroups library coverage — no SmallGroups id.