Finite Group Databasebeta

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C23×C3×C42×C5×C8 #72193375

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 34634616274944
homologyAbelianization (H1) = G · Schur multiplier (H2) = C212×C43

Aliases

abelianC23×C3×C42×C5×C8
multiplicative(ℤ/63960)ˣ, (ℤ/68640)ˣ, (ℤ/68880)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC22×C4C26×C3×C5
socle, prime radicalC26×C3×C5C22×C4
LCSG ▷ C1
UCSC1 ◁ G

222804 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C3×C42×C5×C16, C23×C3×C4×C5×C82, C22×C3×C43×C5×C8, …
maximal normal subgroup ofC23×C3×C42×C5×C16, C23×C3×C4×C5×C82, C22×C3×C43×C5×C8, …
maximal quotient ofC23×C3×C42×C5×C16, C23×C3×C4×C5×C82, C22×C3×C43×C5×C8, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.