Finite Group DatabasebetaFinite Group Databasebeta| order | 2096 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D131 |
| unambiguous semidirect product | C23⋊D131 |
| Fitting | C23×C131 ⋊ C2 |
| Sylow | C131 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D131 |
| commutator, cosocle | C2×C131 | C23 |
| Frattini | C2 | C22×D131 |
| Fitting | C23×C131 | C2 |
| socle | C22×C131 | C22 |
| hypercenter | C23 | D131 |
| hypocenter | C131 | C2×D4 |
| LCS | G ▷ C2×C131 ▷ C131 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1048 |
530 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #16862160, (C22⋊D131)⋊C4, C4×C22⋊D131, … |
| maximal normal subgroup of | #16862160, (C22⋊D131)⋊C4, C4×C22⋊D131, … |
| maximal quotient of | C2×(C2×D131)⋊C4, C2×C22⋊Dic131, C2×Dic131⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2096, 35);