Finite Group DatabasebetaFinite Group Databasebeta| order | 6604 |
| automorphism | Aut(G) order 4992624 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1651 |
| unambiguous semidirect product | C127⋊Dic13 |
| derived, Hall | C13×C127 ⋊ C4 |
| Sylow | C127 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic127 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1651 |
| commutator, hypocenter | C13×C127 | C4 |
| Fitting, socle | C2×C13×C127 | C2 |
| LCS | G ▷ C13×C127 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,127,2|a^2=d,b^a=b^12,c^a=c^1261654 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1651, Dic4953, (C127⋊C3)⋊Dic13, … |
| maximal normal subgroup of | C3×Dic1651, (C127⋊C3)⋊Dic13, #34090437, … |
| maximal quotient of | C3×Dic1651, Dic4953, C5×Dic1651, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6604, 4);