Finite Group DatabasebetaFinite Group Databasebeta| order | 15075 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C3×C5 |
| direct product | C52⋊C3×C67⋊C3 |
| unambiguous semidirect product | (C52×C67⋊C3)⋊C3 |
| unambiguous semidirect product | (C67×C52⋊C3)⋊C3 |
| unambiguous semidirect product | (C52⋊(C67⋊C3))⋊C3 |
| Fitting, socle, derived, Hall | C52×C67 ⋊ C32 |
| Sylow | C67 ⋊ C3×C52⋊C3 |
| Sylow | C52 ⋊ C3×C67⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C67 | C32 |
| LCS | G ▷ C52×C67 | |
| UCS | C1 | |
32 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1005 |
275 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C52⋊C3×D67⋊C3, (C67⋊C3)⋊#3874, #3874×C67⋊C3, … |
| maximal normal subgroup of | C52⋊C3×D67⋊C3, (C67⋊C3)⋊#3874, #3874×C67⋊C3, … |
| maximal quotient of | C2×C52⋊C3×C67⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15075, 10);