Finite Group Databasebeta

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C8×C17×C43 #72185099

order5848
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) = C23×C3×C7×C16 (order 2688) · Inn(G) = C1 · Out(G) = C23×C3×C7×C16
homologyAbelianization (H1) = G · Schur multiplier (H2) = C1

Aliases

cyclicC5848
abelianC8×C17×C43
multiplicative(ℤ/5849)ˣ, (ℤ/11698)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C2×C17×C43
socle, prime radicalC2×C17×C43C4
LCSG ▷ C1
UCSC1 ◁ G

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

5848 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC16×C17×C43, C2×C8×C17×C43, C3×C8×C17×C43, …
maximal normal subgroup ofC16×C17×C43, C2×C8×C17×C43, C3×C8×C17×C43, …
maximal quotient ofC16×C17×C43, C2×C8×C17×C43, C3×C8×C17×C43, …
automorphism group ofC5849, C2×C5849
outer automorphism group ofC5849, C2×C5849

GAP

Past the SmallGroups library coverage — no SmallGroups id.