Finite Group Databasebeta

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C24×C3×C43×C5 #72193379

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 232744621367623680
homologyAbelianization (H1) = G · Schur multiplier (H2) = C218×C43

Aliases

abelianC24×C3×C43×C5

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC23C27×C3×C5
socle, prime radicalC27×C3×C5C23
LCSG ▷ C1
UCSC1 ◁ G

1513812 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 ofC24×C3×C42×C5×C8, C23×C3×C44×C5, C25×C3×C43×C5
maximal normal subgroup ofC24×C3×C42×C5×C8, C23×C3×C44×C5, C25×C3×C43×C5
maximal quotient ofC24×C3×C42×C5×C8, C23×C3×C44×C5, C25×C3×C43×C5

GAP

Past the SmallGroups library coverage — no SmallGroups id.