Finite Group DatabasebetaFinite Group Databasebeta| order | 5044 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C97 · Schur multiplier (H2) = C1 |
| direct product | Dic13×C97 |
| derived, Sylow | C13 ⋊ C4×C97 |
| Hall | C13×C97 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C97 | D13 |
| commutator, hypocenter | C13 | C4×C97 |
| Frattini | C2 | D13×C97 |
| Fitting, socle | C2×C13×C97 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C97 | |
12 conjugacy classes of subgroups.
1552 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic13×C97, C97×Dic39, Dic13×C97⋊C3, … |
| maximal normal subgroup of | C3×Dic13×C97, Dic13×C97⋊C3, C97×Dic13⋊C3, … |
| maximal quotient of | C3×Dic13×C97, C97×Dic39, C5×Dic13×C97, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5044, 2);