Finite Group DatabasebetaFinite Group Databasebeta| order | 1008 |
| isoclinism | isoclinic class of #92694 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×#92695 |
| Hall | C32×C7 ⋊ C2×D4 |
| Sylow | C32 ⋊ C2×D28 |
| Sylow | C7 ⋊ C2×#625 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22 | (C3⋊D3)⋊D7 |
| commutator, cosocle | C2×C32×C7 | C23 |
| Frattini | C2 | C2×(C3⋊D3)⋊D7 |
| Fitting, socle | C22×C32×C7 | C22 |
| hypocenter | C32×C7 | C2×D4 |
| LCS | G ▷ C2×C32×C7 ▷ C32×C7 | |
| UCS | C1 ◁ C22 | |
232 conjugacy classes of subgroups.
| transitive degree | μt(G) = 336 |
102 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1008, 812);