Finite Group DatabasebetaFinite Group Databasebeta| order | 702 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C32 |
| direct product | D13×H(3,𝔽3) |
| Fitting, Hall | C13×H(3,𝔽3) ⋊ C2 |
| Sylow | C13 ⋊ C2×H(3,𝔽3) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C32×D13 |
| commutator, socle, cosocle | C3×C13 | C2×C32 |
| Fitting | C13×H(3,𝔽3) | C2 |
| hypercenter | H(3,𝔽3) | D13 |
| hypocenter | C13 | C2×H(3,𝔽3) |
| LCS | G ▷ C3×C13 ▷ C13 | |
| UCS | C1 ◁ C3 ◁ H(3,𝔽3) | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 117 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | H(3,𝔽3)×#261, #13063973, #13063976, … |
| maximal normal subgroup of | H(3,𝔽3)×#261, #13063973, #13063976, … |
| maximal quotient of | H(3,𝔽3)×Dic13, C2×D13×H(3,𝔽3) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(702, 30);