Finite Group Databasebeta

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C23×C42×C7×C17 #72193258

order15232
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 6341787648
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C4

Aliases

abelianC23×C42×C7×C17
multiplicative(ℤ/57360)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22C25×C7×C17
socle, prime radicalC25×C7×C17C22
LCSG ▷ C1
UCSC1 ◁ G

6000 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15232 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C4×C7×C8×C17, C22×C43×C7×C17, C24×C42×C7×C17
maximal normal subgroup ofC23×C4×C7×C8×C17, C22×C43×C7×C17, C24×C42×C7×C17
maximal quotient ofC23×C4×C7×C8×C17, C22×C43×C7×C17, C24×C42×C7×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.