Finite Group DatabasebetaFinite Group Databasebeta| order | 10972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C211⋊#261 |
| Fitting, socle, derived, Hall | C13×C211 ⋊ C4 |
| Sylow | C211 ⋊ #261 |
| Sylow | C13 ⋊ Dic211 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C211 | C4 |
| prime radical, cosocle | D13×C211 | C2 |
| LCS | G ▷ C13×C211 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13,211|a^2=b,c^a=c^5,d^a=d^210,c^b=c^12847 conjugacy classes — view the full character table.
| maximal subgroup of | #45681793, #45681794, #45681797, … |
| maximal normal subgroup of | #45681793, #45681794, #45681797, … |
| maximal quotient of | C3×C211⋊#261, C3⋊(C211⋊#261) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10972, 7);