Finite Group DatabasebetaFinite Group Databasebeta| order | 5044 |
| automorphism | Aut(G) order 2905344 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic1261 |
| derived, Hall | C13×C97 ⋊ C4 |
| Sylow | C97 ⋊ Dic13 |
| Sylow | C13 ⋊ Dic97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D1261 |
| commutator, hypocenter | C13×C97 | C4 |
| Fitting, socle | C2×C13×C97 | C2 |
| LCS | G ▷ C13×C97 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,13,97,2|a^2=d,b^a=b^12,c^a=c^961264 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic1261, Dic3783, #29502722, … |
| maximal normal subgroup of | C3×Dic1261, #29502722, #29502723, … |
| maximal quotient of | C3×Dic1261, Dic3783, C5×Dic1261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5044, 4);