Finite Group Databasebeta

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C26×C3×C5×C16 #72193369

order15360
nilpotency class1
isoclinismisoclinic class of C1
automorphismAut(G) order 5284484811325440
homologyAbelianization (H1) = G · Schur multiplier (H2) = C221

Aliases

abelianC26×C3×C5×C16

Subgroups

subgroupG/H
centerGC1
commutatorC1G
Frattini, cosocleC8C27×C3×C5
socle, prime radicalC27×C3×C5C8
LCSG ▷ C1
UCSC1 ◁ G

433492 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

15360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC26×C3×C5×C32, C27×C3×C5×C16, C25×C3×C4×C5×C16
maximal normal subgroup ofC26×C3×C5×C32, C27×C3×C5×C16, C25×C3×C4×C5×C16
maximal quotient ofC26×C3×C5×C32, C27×C3×C5×C16, C25×C3×C4×C5×C16

GAP

Past the SmallGroups library coverage — no SmallGroups id.