Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | C2×#14536781 |
| Fitting | C2×C17×#379 ⋊ C2 |
| Sylow | C17 ⋊ C2×#2812 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D17 |
| commutator, cosocle | C23×C17 | C25 |
| Frattini | C23 | C24×D17 |
| Fitting | C2×C17×#379 | C2 |
| socle | C24×C17 | C24 |
| hypercenter | C2×#379 | D17 |
| hypocenter | C17 | C2×#2812 |
| LCS | G ▷ C23×C17 ▷ C17 | |
| UCS | C1 ◁ C24 ◁ C2×#379 | |
4438 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 4438 conjugacy classes of subgroups — too many to draw. Only its 667 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1088 |
500 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 375686);