Finite Group DatabasebetaFinite Group Databasebeta| order | 10396 |
| isoclinism | isoclinic class of #90673 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#90673 |
| Fitting, socle, Hall | C23×C113 ⋊ C4 |
| derived, Sylow | C113 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #90673 |
| commutator, hypocenter | C113 | C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C113 | C4 |
| prime radical | C23×D113 | C2 |
| cosocle | D113 | C2×C23 |
| LCS | G ▷ C113 | |
| UCS | C1 ◁ C23 | |
12 conjugacy classes of subgroups.
736 conjugacy classes — view the full character table.
| maximal subgroup of | C3×C23×#90673, C23×C3⋊#90673 |
| maximal normal subgroup of | C3×C23×#90673 |
| maximal quotient of | C3×C23×#90673, C23×C3⋊#90673 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10396, 6);