Finite Group DatabasebetaFinite Group Databasebeta| order | 1568 |
| isoclinism | isoclinic class of D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#87639 |
| derived, Sylow | C72 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D72 |
| commutator, hypocenter | C72 | C23×C4 |
| Frattini | C2 | C22×D72 |
| Fitting, socle | C23×C72 | C22 |
| prime radical | C23×C7⋊D7 | C2 |
| cosocle | C2×C72 | C24 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C23 | |
673 conjugacy classes of subgroups.
| transitive degree | μt(G) = 112 |
200 conjugacy classes — view the full character table.
| maximal subgroup of | C22×#11716115, C2×D3×#87639, C22×#11924174, … |
| maximal normal subgroup of | C22×#11716115, C22×#11924174, C2×#13096694 |
| maximal quotient of | C2×D3×#87639, C2×#13096284 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1568, 872);