Finite Group DatabasebetaFinite Group Databasebeta| order | 5372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C79⋊#595 |
| Fitting, socle, derived, Hall | C17×C79 ⋊ C4 |
| Sylow | C79 ⋊ #595 |
| Sylow | C17 ⋊ Dic79 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C17×C79 | C4 |
| LCS | G ▷ C17×C79 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,17,79|a^2=b,c^a=c^13,d^a=d^78,c^b=c^16398 conjugacy classes — view the full character table.
| maximal subgroup of | (C79⋊C3)⋊#595, C3×C79⋊#595, C3⋊(C79⋊#595), … |
| maximal normal subgroup of | (C79⋊C3)⋊#595, C3×C79⋊#595, C5×C79⋊#595, … |
| maximal quotient of | C3×C79⋊#595, C3⋊(C79⋊#595), C5×C79⋊#595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5372, 7);