Finite Group DatabasebetaFinite Group Databasebeta| order | 16768 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C131 · Schur multiplier (H2) = C24×C4 |
| direct product | #2273×C131 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C131 | C24 |
| commutator | C2 | C22×C42×C131 |
| Frattini, cosocle | C23 | C24×C131 |
| prime radical | C25×C131 | C22 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ G | |
912 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4192 |
8908 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C131×#8734, C131×#9407, C131×#9409, … |
| maximal normal subgroup of | C131×#8734, C131×#9407, C131×#9409, … |
| maximal quotient of | C131×#13749, C131×#13775, C131×#13778, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(16768, 1005);