Finite Group Databasebeta

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C3×C42×C5×C72 #72190200

order11760
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1548288
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4×C7

Aliases

abelianC3×C42×C5×C72
multiplicative(ℤ/12209)ˣ, (ℤ/24418)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C3×C5×C72
socle, prime radicalC22×C3×C5×C72C22
LCSG ▷ C1
UCSC1 ◁ G

600 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11760 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C5×C72×C8, C2×C3×C42×C5×C72
maximal normal subgroup ofC3×C4×C5×C72×C8, C2×C3×C42×C5×C72
maximal quotient ofC3×C4×C5×C72×C8, C2×C3×C42×C5×C72
automorphism group ofC29×C421
outer automorphism group ofC29×C421

GAP

Past the SmallGroups library coverage — no SmallGroups id.