Finite Group Databasebeta

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C24×C5×C11×C16 #72192240

order14080
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 1651507200
homologyAbelianization (H1) = G · Schur multiplier (H2) = C210

Aliases

abelianC24×C5×C11×C16
multiplicative(ℤ/34408)ˣ, (ℤ/48576)ˣ, (ℤ/49368)ˣ, (ℤ/51612)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C25×C5×C11
socle, prime radicalC25×C5×C11C8
LCSG ▷ C1
UCSC1 ◁ G

5180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

14080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C5×C11×C32, C23×C4×C5×C11×C16, C25×C5×C11×C16
maximal normal subgroup ofC24×C5×C11×C32, C23×C4×C5×C11×C16, C25×C5×C11×C16
maximal quotient ofC24×C5×C11×C32, C23×C4×C5×C11×C16, C25×C5×C11×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.