Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of #5997 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C7 · Schur multiplier (H2) = C7 |
| direct product | C7×#5997 |
| Fitting, socle, Sylow | C73 ⋊ C4 |
| derived | C72 ⋊ C4×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | #5997 |
| commutator, hypocenter | C72 | C4×C7 |
| Frattini | C1 | G |
| Fitting, socle | C73 | C4 |
| prime radical | C7×C7⋊D7 | C2 |
| cosocle | C7⋊D7 | C2×C7 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C7 | |
52 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28 |
112 conjugacy classes — view the full character table.
| maximal subgroup of | #72228141 |
| maximal normal subgroup of | #72228141 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 30);