Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28×C4 |
| direct product | C2×#11739575 |
| Fitting | C23×C7×C22⋊C4 ⋊ C2 |
| Sylow | C7 ⋊ C2×#2617 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C23×C7×C22⋊C4 | C2 |
| socle | C24×C7 | C24 |
| hypercenter | C23×C22⋊C4 | D7 |
| hypocenter | C7 | C2×#2617 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C23×C22⋊C4 | |
5222 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
304 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 335905);