Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C210 |
| direct product | D7×#1438 |
| Fitting | C7×#1438 ⋊ C2 |
| Sylow | C7 ⋊ C2×#1438 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D7 |
| commutator | C23×C7 | C23×C4 |
| Fitting | C7×#1438 | C2 |
| socle, cosocle | C24×C7 | C24 |
| prime radical | C23×D4×D7 | C2 |
| hypercenter | #1438 | D7 |
| hypocenter | C7 | C2×#1438 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ #1438 | |
8190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 448 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D7×#15258, D7×#8534, AGL(1,𝔽7)×#1438, … |
| maximal normal subgroup of | D7×#15258, D7×#8534, AGL(1,𝔽7)×#1438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 91223);