Finite Group Databasebeta

← Prev (#72182153) Next (#72182155) →

C24×C5×C27 #72182154

order2160
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1451520
homologyAbelianization (H1) = G · Schur multiplier (H2) = C26

Aliases

abelianC24×C5×C27
multiplicative(ℤ/6504)ˣ, (ℤ/7128)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC9C24×C3×C5
socle, prime radicalC24×C3×C5C9
LCSG ▷ C1
UCSC1 ◁ G

536 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×C4×C5×C27, C25×C5×C27, C24×C5×C81, …
maximal normal subgroup ofC23×C4×C5×C27, C25×C5×C27, C24×C5×C81, …
maximal quotient ofC23×C4×C5×C27, C25×C5×C27, C24×C5×C81, …
automorphism group ofC3×C8×C271, C8×C11×C81
outer automorphism group ofC3×C8×C271, C8×C11×C81

GAP

Past the SmallGroups library coverage — no SmallGroups id.