Finite Group DatabasebetaFinite Group Databasebeta| order | 4998 |
| isoclinism | isoclinic class of #64418 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17 · Schur multiplier (H2) = C1 |
| direct product | C17×#64418 |
| Fitting, socle, Hall | C72×C17 ⋊ D3 |
| derived, Hall | #3862 ⋊ C2×C17 |
| Hall | C17×#3862 ⋊ C2 |
| Sylow | C72 ⋊ D3×C17 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C17 | #64418 |
| commutator, hypocenter | #3862 | C2×C17 |
| Frattini | C1 | G |
| Fitting, socle | C72×C17 | D3 |
| LCS | G ▷ #3862 | |
| UCS | C1 ◁ C17 | |
28 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | C17×#64418⋊C3, C3×C17×#64418, C17×C3⋊#64418, … |
| maximal normal subgroup of | C17×#64418⋊C3, C3×C17×#64418, C5×C17×#64418 |
| maximal quotient of | C17×#11725071, C3×C17×#64418, C17×C3⋊#64418, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4998, 31);