Finite Group DatabasebetaFinite Group Databasebeta| order | 1264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×Dic158 |
| unambiguous semidirect product | (C2×C79)⋊Q8 |
| Sylow | C79 ⋊ C2×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D79 |
| commutator, cosocle | C2×C79 | C23 |
| Frattini | C2 | C22×D79 |
| Fitting | C2×C4×C79 | C2 |
| socle, prime radical | C22×C79 | C22 |
| hypercenter | C2×C4 | D79 |
| hypocenter | C79 | C2×Q8 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1264 |
322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14579079, #14579084, #14579086, … |
| maximal normal subgroup of | #14579079, #14579084, #14579086, … |
| maximal quotient of | C2×Dic79⋊C4, C2×C4⋊Dic79, C4×Dic158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1264, 38);