Finite Group Databasebeta

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C2×C3×C4×C7×C61 #72188908

order10248
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5760
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C7×C61
multiplicative(ℤ/10643)ˣ, (ℤ/11963)ˣ, (ℤ/15381)ˣ, (ℤ/21286)ˣ, (ℤ/23926)ˣ, (ℤ/30762)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C7×C61
socle, prime radicalC22×C3×C7×C61C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10248 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C42×C7×C61, C2×C3×C7×C8×C61, C22×C3×C4×C7×C61, …
maximal normal subgroup ofC3×C42×C7×C61, C2×C3×C7×C8×C61, C22×C3×C4×C7×C61, …
maximal quotient ofC3×C42×C7×C61, C2×C3×C7×C8×C61, C22×C3×C4×C7×C61, …
automorphism group ofC29×C367, C7×C1709
outer automorphism group ofC29×C367, C7×C1709

GAP

Past the SmallGroups library coverage — no SmallGroups id.