Finite Group DatabasebetaFinite Group Databasebeta| order | 2096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C131 ⋊ C2 |
| Sylow | C131 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D131 |
| commutator, cosocle | C4×C131 | C22 |
| Frattini | C4 | C2×D131 |
| Fitting | D4×C131 | C2 |
| socle | C2×C131 | D4 |
| hypercenter | D4 | D131 |
| hypocenter | C131 | D8 |
| LCS | G ▷ C4×C131 ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 139 |
| transitive degree | μt(G) = 1048 |
Polycyclic presentation:
2^4,131|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^130332 conjugacy classes — view the full character table.
| maximal subgroup of | D8×D131, C2×#14523498, #16862266, … |
| maximal normal subgroup of | D8×D131, C2×#14523498, #16862266, … |
| maximal quotient of | #16862166, #16862167, #16862179, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2096, 25);