Finite Group Databasebeta

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C42×C5×C131 #72189101

order10480
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 49920
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C5×C131
multiplicative(ℤ/13105)ˣ, (ℤ/26210)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C5×C131
socle, prime radicalC22×C5×C131C22
LCSG ▷ C1
UCSC1 ◁ G

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

10480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C8×C131, C2×C42×C5×C131, C3×C42×C5×C131
maximal normal subgroup ofC4×C5×C8×C131, C2×C42×C5×C131, C3×C42×C5×C131
maximal quotient ofC4×C5×C8×C131, C2×C42×C5×C131, C3×C42×C5×C131
automorphism group ofC5×C2621
outer automorphism group ofC5×C2621

GAP

Past the SmallGroups library coverage — no SmallGroups id.