Finite Group DatabasebetaFinite Group Databasebeta| order | 8450 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C5×C13 |
| unambiguous semidirect product | C5⋊(C5⋊(C13⋊D13)) |
| unambiguous semidirect product | C13⋊(C5⋊D65) |
| Fitting, socle, derived, Hall | C52×C132 ⋊ C2 |
| Sylow | C132 ⋊ C5⋊D5 |
| Sylow | C52 ⋊ C13⋊D13 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C132 | C2 |
| LCS | G ▷ C52×C132 | |
| UCS | C1 | |
256 conjugacy classes of subgroups.
Polycyclic presentation:
2,5^2,13^2|b^a=b^4,c^a=c^4,d^a=d^12,e^a=e^122114 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30683447, #30683448, #30683449, … |
| maximal normal subgroup of | #30683447, #30683448, #30683449, … |
| maximal quotient of | #30683418, C2×C5⋊(C5⋊(C13⋊D13)), C3×C5⋊(C5⋊(C13⋊D13)), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8450, 25);