Finite Group DatabasebetaFinite Group Databasebeta| order | 9700 |
| isoclinism | isoclinic class of #1043 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C97 · Schur multiplier (H2) = C1 |
| direct product | C97×#1043 |
| Fitting, socle, Hall | C52×C97 ⋊ C4 |
| derived, Sylow | C52 ⋊ C4×C97 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C97 | #1043 |
| commutator, hypocenter | C52 | C4×C97 |
| Frattini | C1 | G |
| Fitting, socle | C52×C97 | C4 |
| prime radical | C5⋊D5×C97 | C2 |
| cosocle | C5⋊D5 | C2×C97 |
| LCS | G ▷ C52 | |
| UCS | C1 ◁ C97 | |
48 conjugacy classes of subgroups.
970 conjugacy classes — view the full character table.
| maximal subgroup of | C97×#1043⋊C3, #1043⋊(C97⋊C3), #1043×C97⋊C3, … |
| maximal normal subgroup of | C97×#1043⋊C3, #1043⋊(C97⋊C3), #1043×C97⋊C3, … |
| maximal quotient of | C3×C97×#1043, C97×C3⋊#1043 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9700, 30);