Finite Group DatabasebetaFinite Group Databasebeta| order | 1372 |
| isoclinism | isoclinic class of D72 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7 · Schur multiplier (H2) = C2 |
| direct product | C7×D72 |
| unambiguous semidirect product | (C7×D7)⋊(C2×C7) |
| Fitting, socle, Sylow | C73 ⋊ C22 |
| derived | C72 ⋊ C22×C7 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C7 | D72 |
| commutator, cosocle, hypocenter | C72 | C22×C7 |
| Frattini | C1 | G |
| Fitting, socle | C73 | C22 |
| LCS | G ▷ C72 | |
| UCS | C1 ◁ C7 | |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 28 |
175 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#64423⋊C2, D72×ΓL(1,𝔽8), #72259063, … |
| maximal normal subgroup of | C7×#64423⋊C2, D72×ΓL(1,𝔽8), #72259063, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1372, 32);