Finite Group Databasebeta

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C2×C3×C43×C17 #72185665

order6528
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 176160768
homologyAbelianization (H1) = G · Schur multiplier (H2) = C23×C43

Aliases

abelianC2×C3×C43×C17

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C24×C3×C17
socle, prime radicalC24×C3×C17C23
LCSG ▷ C1
UCSC1 ◁ G

2544 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6528 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C3×C42×C8×C17, C3×C44×C17, C22×C3×C43×C17, …
maximal normal subgroup ofC2×C3×C42×C8×C17, C3×C44×C17, C22×C3×C43×C17, …
maximal quotient ofC2×C3×C42×C8×C17, C3×C44×C17, C22×C3×C43×C17, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.