Finite Group Databasebeta

← Prev (#72190665) Next (#72190667) →

C25×C3×C4×C32 #72190666

order12288
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 10736731045232640
homologyAbelianization (H1) = G · Schur multiplier (H2) = C220×C4

Aliases

abelianC25×C3×C4×C32

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC2×C16C27×C3
socle, prime radicalC27×C3C2×C16
LCSG ▷ C1
UCSC1 ◁ G

705270 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 ofC25×C3×C4×C64, C25×C3×C8×C32, C24×C3×C42×C32, …
maximal normal subgroup ofC25×C3×C4×C64, C25×C3×C8×C32, C24×C3×C42×C32, …
maximal quotient ofC25×C3×C4×C64, C25×C3×C8×C32, C24×C3×C42×C32, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.