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C2×C3×C4×C5×C8×C13 #72190824

order12480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 196608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C4×C5×C8×C13
multiplicative(ℤ/15211)ˣ, (ℤ/16195)ˣ, (ℤ/17215)ˣ, (ℤ/18235)ˣ, (ℤ/19311)ˣ, (ℤ/19557)ˣ, (ℤ/20319)ˣ, (ℤ/20787)ˣ, (ℤ/23445)ˣ, (ℤ/23475)ˣ, (ℤ/25748)ˣ, (ℤ/27092)ˣ, (ℤ/27716)ˣ, (ℤ/30422)ˣ, (ℤ/31300)ˣ, (ℤ/32390)ˣ, (ℤ/34430)ˣ, (ℤ/36470)ˣ, (ℤ/38622)ˣ, (ℤ/39114)ˣ, (ℤ/40638)ˣ, (ℤ/41574)ˣ, (ℤ/46890)ˣ, (ℤ/46950)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C4C23×C3×C5×C13
socle, prime radicalC23×C3×C5×C13C2×C4
LCSG ▷ C1
UCSC1 ◁ G

648 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C5×C13×C16, C2×C3×C5×C82×C13, C3×C42×C5×C8×C13, …
maximal normal subgroup ofC2×C3×C4×C5×C13×C16, C2×C3×C5×C82×C13, C3×C42×C5×C8×C13, …
maximal quotient ofC2×C3×C4×C5×C13×C16, C2×C3×C5×C82×C13, C3×C42×C5×C8×C13, …
automorphism group ofC7×C41×C53
outer automorphism group ofC7×C41×C53

GAP

Past the SmallGroups library coverage — no SmallGroups id.