Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C212×C4 |
| direct product | C22×#11763525 |
| Fitting | C22×C17×C4⋊Q8 ⋊ C2 |
| Sylow | C17 ⋊ C22×#555 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D17 |
| commutator, cosocle | C22×C17 | C26 |
| Frattini | C22 | C25×D17 |
| Fitting | C22×C17×C4⋊Q8 | C2 |
| socle | C24×C17 | C24 |
| hypercenter | C22×C4⋊Q8 | D17 |
| hypocenter | C17 | C22×#555 |
| LCS | G ▷ C22×C17 ▷ C17 | |
| UCS | C1 ◁ C24 ◁ C22×C4⋊Q8 | |
8710 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2176 |
548 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1076588);