Finite Group Databasebeta

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C2×C3×C4×C7×C59 #72188591

order9912
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5568
homologyAbelianization (H1) = G · Schur multiplier (H2) = C2

Aliases

abelianC2×C3×C4×C7×C59
multiplicative(ℤ/10751)ˣ, (ℤ/14871)ˣ, (ℤ/19828)ˣ, (ℤ/21502)ˣ, (ℤ/29742)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2C22×C3×C7×C59
socle, prime radicalC22×C3×C7×C59C2
LCSG ▷ C1
UCSC1 ◁ G

64 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9912 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C7×C8×C59, C3×C42×C7×C59, C22×C3×C4×C7×C59, …
maximal normal subgroup ofC2×C3×C7×C8×C59, C3×C42×C7×C59, C22×C3×C4×C7×C59, …
maximal quotient ofC2×C3×C7×C8×C59, C3×C42×C7×C59, C22×C3×C4×C7×C59, …
automorphism group ofC13×C827
outer automorphism group ofC13×C827

GAP

Past the SmallGroups library coverage — no SmallGroups id.