Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#22578064 |
| Fitting | C23×Q8×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×#548 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D137 |
| commutator, cosocle | C22×C137 | C25 |
| Frattini | C22 | C24×D137 |
| Fitting | C23×Q8×C137 | C2 |
| socle | C23×C137 | C24 |
| hypercenter | C23×Q8 | D137 |
| hypocenter | C137 | C2×#548 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C23×Q8 | |
1620 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
2770 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 17978);