Finite Group DatabasebetaFinite Group Databasebeta| order | 8138 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C13 · Schur multiplier (H2) = C1 |
| direct product | C13×D313 |
| Fitting, socle, Hall | C13×C313 ⋊ C2 |
| derived, Sylow | C313 ⋊ C2×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C13 | D313 |
| commutator, hypocenter | C313 | C2×C13 |
| Frattini | C1 | G |
| Fitting, socle | C13×C313 | C2 |
| LCS | G ▷ C313 | |
| UCS | C1 ◁ C13 | |
8 conjugacy classes of subgroups.
2054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C13×#11929411, #30653710, D13×D313, … |
| maximal normal subgroup of | C13×#11929411, #30653710, D13×D313, … |
| maximal quotient of | C13×Dic313, C2×C13×D313, C3×C13×D313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8138, 4);