Finite Group DatabasebetaFinite Group Databasebeta| order | 2096 |
| isoclinism | isoclinic class of D131 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D131 |
| Fitting | C8×C131 ⋊ C2 |
| derived, Sylow | C131 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D131 |
| commutator, hypocenter | C131 | C2×C8 |
| Frattini | C4 | C2×D131 |
| Fitting | C8×C131 | C2 |
| socle | C2×C131 | C2×C4 |
| prime radical | C2×D131 | C4 |
| cosocle | C4×C131 | C22 |
| LCS | G ▷ C131 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1048 |
536 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D131, #16862185, C2×C8×D131, … |
| maximal normal subgroup of | C16×D131, #16862185, C2×C8×D131, … |
| maximal quotient of | C8×Dic131, (C2×D131)⋊C8, Dic131⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2096, 21);