Finite Group Databasebeta

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C24×C3×C4×C64 #72190653

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 2705829396480
homologyAbelianization (H1) = G · Schur multiplier (H2) = C214×C4

Aliases

abelianC24×C3×C4×C64

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C32C26×C3
socle, prime radicalC26×C3C2×C32
LCSG ▷ C1
UCSC1 ◁ G

77942 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

12288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC24×C3×C4×C128, C24×C3×C8×C64, C25×C3×C4×C64, …
maximal normal subgroup ofC24×C3×C4×C128, C24×C3×C8×C64, C25×C3×C4×C64, …
maximal quotient ofC24×C3×C4×C128, C24×C3×C8×C64, C25×C3×C4×C64, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.