Finite Group DatabasebetaFinite Group Databasebeta| order | 5415 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#11762245 |
| Fitting, socle, Hall | C5×C192 ⋊ C3 |
| derived, Sylow | C192 ⋊ C3×C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #11762245 |
| commutator, hypocenter | C192 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C192 | C3 |
| LCS | G ▷ C192 | |
| UCS | C1 ◁ C5 | |
88 conjugacy classes of subgroups.
615 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#14524206, C5×#14524208, C5⋊#14524206, … |
| maximal normal subgroup of | C5×#14524206, C5×#14524208, C5⋊#14524206, … |
| maximal quotient of | C2×C5×#11762245, C5×#15692429, C3×C5×#11762245, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5415, 7);