Finite Group Databasebeta

← Prev (#72188225) Next (#72188227) →

C2×C3×C4×C5×C79 #72188226

order9480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 4992
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C5×C79
multiplicative(ℤ/9827)ˣ, (ℤ/11855)ˣ, (ℤ/19654)ˣ, (ℤ/23710)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C5×C79
socle, prime radicalC22×C3×C5×C79C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C42×C5×C79, C2×C3×C5×C8×C79, C22×C3×C4×C5×C79, …
maximal normal subgroup ofC3×C42×C5×C79, C2×C3×C5×C8×C79, C22×C3×C4×C5×C79, …
maximal quotient ofC3×C42×C5×C79, C2×C3×C5×C8×C79, C22×C3×C4×C5×C79, …
automorphism group ofC31×C317, C5×C2371
outer automorphism group ofC31×C317, C5×C2371

GAP

Past the SmallGroups library coverage — no SmallGroups id.