Finite Group DatabasebetaFinite Group Databasebeta| order | 784 |
| isoclinism | isoclinic class of Dic98 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D49 |
| unambiguous semidirect product | C23⋊D49 |
| Fitting | C23×C49 ⋊ C2 |
| Sylow | C49 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D49 |
| commutator, cosocle | C2×C49 | C23 |
| Frattini | C2×C7 | C22×D7 |
| Fitting | C23×C49 | C2 |
| socle | C22×C7 | C2×D7 |
| hypercenter | C23 | D49 |
| hypocenter | C49 | C2×D4 |
| LCS | G ▷ C2×C49 ▷ C49 | |
| UCS | C1 ◁ C22 ◁ C23 | |
81 conjugacy classes of subgroups.
| transitive degree | μt(G) = 392 |
202 conjugacy classes — view the full character table.
| maximal subgroup of | #13095846, #13095908, (C22⋊D49)⋊C4, … |
| maximal normal subgroup of | #13095846, #13095908, (C22⋊D49)⋊C4, … |
| maximal quotient of | C2×Dic49⋊C4, #13095953, C2×(C2×D49)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(784, 36);