Finite Group DatabasebetaFinite Group Databasebeta| order | 1696 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | #41×D53 |
| Fitting | #41×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C22×D53 |
| commutator, socle, cosocle | C2×C53 | C24 |
| Frattini | C2 | C23×D53 |
| Fitting | #41×C53 | C2 |
| hypercenter | #41 | D53 |
| hypocenter | C53 | C2×#41 |
| LCS | G ▷ C2×C53 ▷ C53 | |
| UCS | C1 ◁ C4 ◁ #41 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 424 |
280 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×D53, #16810638, #131×D53, … |
| maximal normal subgroup of | #104×D53, #16810638, #131×D53, … |
| maximal quotient of | #117×D53, C4×D4×D53, C4×Q8×D53, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1696, 187);