Finite Group Databasebeta

← Prev (#72187581) Next (#72187583) →

C2×C3×C42×C7×C13 #72187582

order8736
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 221184
homologyAbelianization (H1) = G · Schur multiplier (H2) = C22×C4

Aliases

abelianC2×C3×C42×C7×C13
multiplicative(ℤ/10759)ˣ, (ℤ/11395)ˣ, (ℤ/11455)ˣ, (ℤ/12985)ˣ, (ℤ/13659)ˣ, (ℤ/13833)ˣ, (ℤ/14703)ˣ, (ℤ/16395)ˣ, (ℤ/17488)ˣ, (ℤ/18212)ˣ, (ℤ/19604)ˣ, (ℤ/21518)ˣ, (ℤ/21860)ˣ, (ℤ/22790)ˣ, (ℤ/22910)ˣ, (ℤ/25970)ˣ, (ℤ/27318)ˣ, (ℤ/27666)ˣ, (ℤ/29406)ˣ, (ℤ/32790)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C23×C3×C7×C13
socle, prime radicalC23×C3×C7×C13C22
LCSG ▷ C1
UCSC1 ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C4×C7×C8×C13, C3×C43×C7×C13, C22×C3×C42×C7×C13, …
maximal normal subgroup ofC2×C3×C4×C7×C8×C13, C3×C43×C7×C13, C22×C3×C42×C7×C13, …
maximal quotient ofC2×C3×C4×C7×C8×C13, C3×C43×C7×C13, C22×C3×C42×C7×C13, …
automorphism group ofC7×C29×C53, C5×C43×C53, C5×C29×C79
outer automorphism group ofC7×C29×C53, C5×C43×C53, C5×C29×C79

GAP

Past the SmallGroups library coverage — no SmallGroups id.