Finite Group Databasebeta

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C23×C8×C11×C16 #72189771

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 14092861440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C29×C8

Aliases

abelianC23×C8×C11×C16
multiplicative(ℤ/36312)ˣ, (ℤ/37536)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC4×C8C25×C11
socle, prime radicalC25×C11C4×C8
LCSG ▷ C1
UCSC1 ◁ G

12010 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

11264 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC23×C8×C11×C32, C23×C11×C162, C24×C8×C11×C16, …
maximal normal subgroup ofC23×C8×C11×C32, C23×C11×C162, C24×C8×C11×C16, …
maximal quotient ofC23×C8×C11×C32, C23×C11×C162, C24×C8×C11×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.