Finite Group Databasebeta

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C3×C5×C16×C29 #72186053

order6960
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C22×C43×C7 (order 1792) · Inn(G) = C1 · Out(G) = C22×C43×C7
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC6960
abelianC3×C5×C16×C29
multiplicative(ℤ/6961)ˣ, (ℤ/13922)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C2×C3×C5×C29
socle, prime radicalC2×C3×C5×C29C8
LCSG ▷ C1
UCSC1 ◁ G

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6960 conjugacy classes. The character table is too large to display.

Relationships

derived subgroup ofD13920, Dic6960
maximal subgroup ofC3×C5×C29×C32, C2×C3×C5×C16×C29, C5×C9×C16×C29, …
maximal normal subgroup ofC3×C5×C29×C32, C2×C3×C5×C16×C29, C5×C9×C16×C29, …
maximal quotient ofC3×C5×C29×C32, C2×C3×C5×C16×C29, C5×C9×C16×C29, …
automorphism group ofC6961
outer automorphism group ofC6961

GAP

Past the SmallGroups library coverage — no SmallGroups id.