Finite Group DatabasebetaFinite Group Databasebeta| order | 6100 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#11927415 |
| Fitting, socle, Hall | C52×C61 ⋊ C4 |
| derived | C5×C61 ⋊ C4×C5 |
| Sylow | C61 ⋊ C5×Dic5 |
| Sylow | C52 ⋊ #6923 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11927415 |
| commutator, hypocenter | C5×C61 | C4×C5 |
| Frattini | C1 | G |
| Fitting, socle | C52×C61 | C4 |
| LCS | G ▷ C5×C61 | |
| UCS | C1 ◁ C5 | |
32 conjugacy classes of subgroups.
415 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#11927415⋊C3, #32913047, C3×C5×#11927415, … |
| maximal normal subgroup of | C5×#11927415⋊C3, C3×C5×#11927415 |
| maximal quotient of | C3×C5×#11927415, C5×C3⋊#11927415 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6100, 48);