Finite Group DatabasebetaFinite Group Databasebeta| order | 1264 |
| isoclinism | isoclinic class of D79 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×D79 |
| Fitting | C2×C4×C79 ⋊ C2 |
| derived, Sylow | C79 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | D79 |
| commutator, hypocenter | C79 | C22×C4 |
| Frattini | C2 | C22×D79 |
| Fitting | C2×C4×C79 | C2 |
| socle | C22×C79 | C22 |
| prime radical | C22×D79 | C2 |
| cosocle | C2×C79 | C23 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C2×C4 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 632 |
328 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D79)⋊C8, C42×D79, C22⋊C4×D79, … |
| maximal normal subgroup of | (C2×D79)⋊C8, C42×D79, C22⋊C4×D79, … |
| maximal quotient of | C42×D79, C2×C4×Dic79, C22⋊C4×D79, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1264, 32);