Finite Group DatabasebetaFinite Group Databasebeta| order | 702 |
| isoclinism | isoclinic class of D13 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C33×D13 |
| Fitting, socle, Hall | C33×C13 ⋊ C2 |
| derived, Sylow | C13 ⋊ C2×C33 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C33 | D13 |
| commutator, cosocle, hypocenter | C13 | C2×C33 |
| Frattini | C1 | G |
| Fitting, socle | C33×C13 | C2 |
| LCS | G ▷ C13 | |
| UCS | C1 ◁ C33 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 351 |
216 conjugacy classes — view the full character table.
| maximal subgroup of | C33×#261, C32×C3⋊#261, C3×C3⋊(C3⋊#261), … |
| maximal normal subgroup of | C33×#261, C32×C3⋊#261, C3×C3⋊(C3⋊#261), … |
| maximal quotient of | C33×Dic13, C2×C33×D13 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(702, 55);