Finite Group Databasebeta

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C24×C33×C5 #72182157

order2160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 905748480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26×C33

Aliases

abelianC24×C33×C5
multiplicative(ℤ/7812)ˣ

Subgroups

subgroupG/H
centerGC1
commutator, FrattiniC1G
LCSG ▷ C1
UCSC1 ◁ G

3752 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2160 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C33×C4×C5, C25×C33×C5, C24×C32×C5×C9, …
maximal normal subgroup ofC23×C33×C4×C5, C25×C33×C5, C24×C32×C5×C9, …
maximal quotient ofC23×C33×C4×C5, C25×C33×C5, C24×C32×C5×C9, …
automorphism group ofC4×C7×C9×C31
outer automorphism group ofC4×C7×C9×C31

GAP

Past the SmallGroups library coverage — no SmallGroups id.