Finite Group DatabasebetaFinite Group Databasebeta| order | 26508 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| direct product | C2×#27210411 |
| Fitting, socle | C2×C472 ⋊ D3 |
| derived, Hall | C472⋊C3 ⋊ C22 |
| Sylow | C472 ⋊ C2×D3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #27210411 |
| commutator, cosocle, hypocenter | C472⋊C3 | C22 |
| Frattini | C1 | G |
| Fitting, socle | C2×C472 | D3 |
| LCS | G ▷ C472⋊C3 | |
| UCS | C1 ◁ C2 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 282 |
880 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26508, 24);