Finite Group Databasebeta

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C24×C4×C11×C16 #72189774

order11264
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 3382286745600
homologyAbelianization (H1) = G · Schur multiplier (H2) = C214×C4

Aliases

abelianC24×C4×C11×C16
multiplicative(ℤ/46920)ˣ

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C8C26×C11
socle, prime radicalC26×C11C2×C8
LCSG ▷ C1
UCSC1 ◁ G

50986 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 ofC24×C4×C11×C32, C24×C8×C11×C16, C23×C42×C11×C16, …
maximal normal subgroup ofC24×C4×C11×C32, C24×C8×C11×C16, C23×C42×C11×C16, …
maximal quotient ofC24×C4×C11×C32, C24×C8×C11×C16, C23×C42×C11×C16, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.