Finite Group DatabasebetaFinite Group Databasebeta| order | 10388 |
| automorphism | Aut(G) order 11343696 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2597 |
| unambiguous semidirect product | C49⋊Dic53 |
| derived, Hall | C49×C53 ⋊ C4 |
| Sylow | C53 ⋊ Dic49 |
| Sylow | C49 ⋊ Dic53 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2597 |
| commutator, hypocenter | C49×C53 | C4 |
| Frattini | C2×C7 | D371 |
| Fitting, cosocle | C2×C49×C53 | C2 |
| socle, prime radical | C2×C7×C53 | D7 |
| LCS | G ▷ C49×C53 | |
| UCS | C1 ◁ C2 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2,7,53,2,7|a^2=d,b^7=e^6,b^a=b^6e,c^a=c^52,e^a=e^62600 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2597, Dic7791, (C49⋊C3)⋊Dic53, … |
| maximal normal subgroup of | C3×Dic2597, (C49⋊C3)⋊Dic53, Dic5194 |
| maximal quotient of | C3×Dic2597, Dic7791, Dic12985 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10388, 4);