Finite Group DatabasebetaFinite Group Databasebeta| order | 10348 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C199⋊#261 |
| Fitting, socle, derived, Hall | C13×C199 ⋊ C4 |
| Sylow | C199 ⋊ #261 |
| Sylow | C13 ⋊ Dic199 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C199 | C4 |
| prime radical, cosocle | D13×C199 | C2 |
| LCS | G ▷ C13×C199 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13,199|a^2=b,c^a=c^5,d^a=d^198,c^b=c^12799 conjugacy classes — view the full character table.
| maximal subgroup of | #44526813, #44526814, #44526817, … |
| maximal normal subgroup of | #44526813, #44526814, #44526817, … |
| maximal quotient of | C3×C199⋊#261, C3⋊(C199⋊#261) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10348, 7);