Finite Group DatabasebetaFinite Group Databasebeta| order | 15075 |
| isoclinism | isoclinic class of C67⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C52 · Schur multiplier (H2) = C3×C5 |
| Fitting, socle | C3×C52×C67 ⋊ C3 |
| derived, Sylow | C67 ⋊ C32×C52 |
| Hall | C52×C67 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C52 | C67⋊C3 |
| commutator, cosocle, hypocenter | C67 | C32×C52 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C67 | C3 |
| LCS | G ▷ C67 | |
| UCS | C1 ◁ C3×C52 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5025 |
1875 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×C52×D67⋊C3, C3×C5×C5⋊(D67⋊C3), C3×C5×D5×C67⋊C3, … |
| maximal normal subgroup of | C3×C52×D67⋊C3, C3×C5×C5⋊(D67⋊C3), C3×C5×D5×C67⋊C3, … |
| maximal quotient of | C2×C3×C52×C67⋊C3 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(15075, 13);