Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#14526996 |
| Fitting | C2×C17×D32 ⋊ C2 |
| Sylow | C17 ⋊ C2×D64 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #11762644 |
| commutator, cosocle | C17×C32 | C23 |
| Frattini | C32 | C22×D17 |
| Fitting | C2×C17×D32 | C2 |
| socle | C22×C17 | D32 |
| hypercenter | C2×D32 | D17 |
| hypocenter | C17 | C2×D64 |
| LCS | G ▷ C17×C32 ▷ C16×C17 ▷ C8×C17 ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ C2×D32 | |
142 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 51 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 2176 |
374 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 90610);