Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of #87640 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
| direct product | C22×#87640 |
| Sylow | C72 ⋊ C22×D4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D72 |
| commutator, cosocle | C2×C72 | C24 |
| Frattini | C2 | C22×D72 |
| Fitting, socle | C23×C72 | C22 |
| hypocenter | C72 | C22×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C23 | |
553 conjugacy classes of subgroups.
| transitive degree | μt(G) = 224 |
188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 873);