Finite Group DatabasebetaFinite Group Databasebeta| order | 26772 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1 |
| direct product | C23×#87604⋊C3 |
| unambiguous semidirect product | #87604⋊(C3×C23) |
| unambiguous semidirect product | (C23×#87604)⋊C3 |
| Fitting, socle, Hall | C23×C97 ⋊ C3×C4 |
| derived, Sylow | C97 ⋊ C3×C4×C23 |
| Hall | C23×#87604 ⋊ C3 |
| Hall | C23×C97⋊C3 ⋊ C4 |
| Hall | #87604 ⋊ C3×C23 |
| Hall | C97⋊C3 ⋊ C4×C23 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #87604⋊C3 |
| commutator, hypocenter | C97 | C3×C4×C23 |
| Frattini | C1 | G |
| Fitting, socle | C23×C97 | C3×C4 |
| prime radical | C23×D97⋊C3 | C2 |
| cosocle | D97 | C2×C3×C23 |
| LCS | G ▷ C97 | |
| UCS | C1 ◁ C23 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2231 |
460 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26772, 14);