Finite Group Databasebeta

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C23×C3×C5×C8×C17 #72194251

order16320
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5505024
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC23×C3×C5×C8×C17
multiplicative(ℤ/31647)ˣ, (ℤ/33784)ˣ, (ℤ/33976)ˣ, (ℤ/35992)ˣ, (ℤ/36256)ˣ, (ℤ/42196)ˣ, (ℤ/50676)ˣ, (ℤ/50964)ˣ, (ℤ/53988)ˣ, (ℤ/54252)ˣ, (ℤ/63294)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4C24×C3×C5×C17
socle, prime radicalC24×C3×C5×C17C4
LCSG ▷ C1
UCSC1 ◁ G

1352 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

16320 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C5×C16×C17, C22×C3×C4×C5×C8×C17, C24×C3×C5×C8×C17
maximal normal subgroup ofC23×C3×C5×C16×C17, C22×C3×C4×C5×C8×C17, C24×C3×C5×C8×C17
maximal quotient ofC23×C3×C5×C16×C17, C22×C3×C4×C5×C8×C17, C24×C3×C5×C8×C17

GAP

Past the SmallGroups library coverage — no SmallGroups id.