Finite Group DatabasebetaFinite Group Databasebeta| order | 7004 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C17 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | Dic103⋊C17 |
| unambiguous semidirect product | (C103⋊C17)⋊C4 |
| derived, Sylow | C103 ⋊ C4×C17 |
| Hall | C103⋊C17 ⋊ C4 |
| Hall | Dic103 ⋊ C17 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D103⋊C17 |
| commutator, hypocenter | C103 | C4×C17 |
| Fitting, socle | C2×C103 | C2×C17 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,17,103,2|a^2=d,c^a=c^102,c^b=c^7274 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7004, 2);