Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#11716041 |
| Sylow | C72 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D72 |
| commutator | C2×C72 | C22×C4 |
| Frattini | C22 | C2×D72 |
| Fitting, socle | C23×C72 | C22 |
| prime radical | C23×C7⋊D7 | C2 |
| cosocle | C22×C72 | C23 |
| hypocenter | C72 | C2×C22⋊C4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C23 | |
465 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 563);