Finite Group DatabasebetaFinite Group Databasebeta| order | 17152 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C213 |
| direct product | C2×#22574171 |
| Fitting | C2×D4×Q8×C67 ⋊ C2 |
| Sylow | C67 ⋊ C2×#3514 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C24×D67 |
| commutator, cosocle | C22×C67 | C26 |
| Frattini | C22 | C25×D67 |
| Fitting | C2×D4×Q8×C67 | C2 |
| socle | C23×C67 | C25 |
| hypercenter | C2×D4×Q8 | D67 |
| hypocenter | C67 | C2×#3514 |
| LCS | G ▷ C22×C67 ▷ C67 | |
| UCS | C1 ◁ C23 ◁ C2×D4×Q8 | |
8006 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4288 |
1738 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17152, 1077666);