Finite Group Databasebeta

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C42×C5×C7×C17 #72188259

order9520
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 36864
homologyAbelianization (H1) = G · Schur multiplier (H2) = C4

Aliases

abelianC42×C5×C7×C17
multiplicative(ℤ/11905)ˣ, (ℤ/23810)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C22×C5×C7×C17
socle, prime radicalC22×C5×C7×C17C22
LCSG ▷ C1
UCSC1 ◁ G

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C7×C8×C17, C2×C42×C5×C7×C17, C3×C42×C5×C7×C17
maximal normal subgroup ofC4×C5×C7×C8×C17, C2×C42×C5×C7×C17, C3×C42×C5×C7×C17
maximal quotient ofC4×C5×C7×C8×C17, C2×C42×C5×C7×C17, C3×C42×C5×C7×C17
automorphism group ofC5×C2381
outer automorphism group ofC5×C2381

GAP

Past the SmallGroups library coverage — no SmallGroups id.