Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| isoclinism | isoclinic class of #6157 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#6157 |
| unambiguous semidirect product | D53⋊C42 |
| Fitting | C2×C4×C53 ⋊ C4 |
| derived, Sylow | C53 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #6157 |
| commutator, hypocenter | C53 | C2×C42 |
| Frattini | C2 | C22×#6157 |
| Fitting | C2×C4×C53 | C4 |
| socle | C22×C53 | C2×C4 |
| prime radical | C22×D53 | C22 |
| cosocle | C2×D53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
136 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#6157)⋊C8, #16811493, #16811495, … |
| maximal normal subgroup of | (C2×#6157)⋊C8, #16811493, #16811495, … |
| maximal quotient of | C42×#6157, C2×(C2×#6157)⋊C4, #16811559, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 222);