Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | M16×#1131 |
| Fitting | C7×C8×M16 ⋊ C2 |
| Sylow | C7 ⋊ M162 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C42 | C23×D7 |
| commutator, socle | C22×C7 | C22×C42 |
| Fitting | C7×C8×M16 | C2 |
| prime radical | C23×D7 | C42 |
| cosocle | C42×C7 | C24 |
| hypercenter | C8×M16 | D7 |
| hypocenter | C7 | M162 |
| LCS | G ▷ C22×C7 ▷ C7 | |
| UCS | C1 ◁ C42 ◁ C8×M16 | |
900 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
340 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 135276);