Finite Group DatabasebetaFinite Group Databasebeta| order | 572 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C11 · Schur multiplier (H2) = C1 |
| direct product | C11×Dic13 |
| derived, Sylow | C13 ⋊ C4×C11 |
| Hall | C11×C13 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C11 | D13 |
| commutator, hypocenter | C13 | C4×C11 |
| Frattini | C2 | C11×D13 |
| Fitting, socle, prime radical | C2×C11×C13 | C2 |
| cosocle | C2×C13 | C2×C11 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C2×C11 | |
12 conjugacy classes of subgroups.
| transitive degree | μt(G) = 572 |
176 conjugacy classes — view the full character table.
| maximal subgroup of | C11×#1057, C11⋊#1057, D11×Dic13, … |
| maximal normal subgroup of | C11×#1057, C11⋊#1057, D11×Dic13, … |
| maximal quotient of | C11×#1055, C2×C11×Dic13, C3×C11×Dic13, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(572, 2);