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C2×C3×C4×C5×C7×C13 #72189462

order10920
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4608
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C5×C7×C13
multiplicative(ℤ/11147)ˣ, (ℤ/11183)ˣ, (ℤ/11843)ˣ, (ℤ/11999)ˣ, (ℤ/12023)ˣ, (ℤ/13655)ˣ, (ℤ/13675)ˣ, (ℤ/22294)ˣ, (ℤ/22366)ˣ, (ℤ/23686)ˣ, (ℤ/23998)ˣ, (ℤ/24046)ˣ, (ℤ/27310)ˣ, (ℤ/27350)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C5×C7×C13
socle, prime radicalC22×C3×C5×C7×C13C2
LCSG ▷ C1
UCSC1 ◁ G

128 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10920 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C5×C7×C8×C13, C3×C42×C5×C7×C13, C22×C3×C4×C5×C7×C13, …
maximal normal subgroup ofC2×C3×C5×C7×C8×C13, C3×C42×C5×C7×C13, C22×C3×C4×C5×C7×C13, …
maximal quotient ofC2×C3×C5×C7×C8×C13, C3×C42×C5×C7×C13, C22×C3×C4×C5×C7×C13, …
automorphism group ofC71×C157, C53×C211, C13×C911, …
outer automorphism group ofC71×C157, C53×C211, C13×C911, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.