Finite Group DatabasebetaFinite Group Databasebeta| order | 17768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#22580075 |
| unambiguous semidirect product | D2221⋊C4 |
| Fitting, socle | C2×C2221 ⋊ C4 |
| derived, Sylow | C2221 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #22580075 |
| commutator, hypocenter | C2221 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C2221 | C4 |
| prime radical | C2×D2221 | C2 |
| cosocle | D2221 | C22 |
| LCS | G ▷ C2221 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4442 |
1118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#22580075, C22⋊#22580075, C4⋊#22580075, … |
| maximal normal subgroup of | C4×#22580075, C22⋊#22580075, C4⋊#22580075, … |
| maximal quotient of | C4×#22580075, C22⋊#22580075, C4⋊#22580075, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17768, 14);