Finite Group DatabasebetaFinite Group Databasebeta| order | 1264 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C22⋊D79 |
| unambiguous semidirect product | C23⋊D79 |
| Fitting | C23×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D79 |
| commutator, cosocle | C2×C79 | C23 |
| Frattini | C2 | C22×D79 |
| Fitting | C23×C79 | C2 |
| socle | C22×C79 | C22 |
| hypercenter | C23 | D79 |
| hypocenter | C79 | C2×D4 |
| LCS | G ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C23 | |
54 conjugacy classes of subgroups.
| transitive degree | μt(G) = 632 |
322 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14579075, (C22⋊D79)⋊C4, C4×C22⋊D79, … |
| maximal normal subgroup of | #14579075, (C22⋊D79)⋊C4, C4×C22⋊D79, … |
| maximal quotient of | C2×(C2×D79)⋊C4, C2×C22⋊Dic79, C2×Dic79⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1264, 35);