Finite Group DatabasebetaFinite Group Databasebeta| order | 16256 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1304 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C127 · Schur multiplier (H2) = C2 |
| direct product | C127×#1308 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C127 | #95 |
| commutator | C23 | C42×C127 |
| Frattini, cosocle | C2×C42 | C22×C127 |
| prime radical | C23×C127 | C42 |
| LCS | G ▷ C23 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C127 ◁ C2×C42×C127 ◁ G | |
122 conjugacy classes of subgroups.
3302 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C127×#1308, C127×#8124, C127×#8125, … |
| maximal normal subgroup of | C2×C127×#1308, C127×#8124, C127×#8125, … |
| maximal quotient of | C127×#7033, C127×#7041, C127×#7048, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16256, 40);