Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23×C7 |
| direct product | D4×C7⋊Dic7 |
| Sylow | C72 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×C7⋊D7 |
| commutator | C2×C72 | C22×C4 |
| Fitting, prime radical | C2×C72×D4 | C2 |
| socle, cosocle | C22×C72 | C23 |
| hypercenter | C2×D4 | C7⋊D7 |
| hypocenter | C72 | C4×D4 |
| LCS | G ▷ C2×C72 ▷ C72 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
470 conjugacy classes of subgroups.
| transitive degree | μt(G) = 784 |
260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #72259476, C4×D4×C7⋊D7, #72259560, … |
| maximal normal subgroup of | #72259476, C4×D4×C7⋊D7, #72259560, … |
| maximal quotient of | #72259476 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 737);