Finite Group DatabasebetaFinite Group Databasebeta| order | 26272 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×#15692846 |
| unambiguous semidirect product | D821⋊(C22×C4) |
| Fitting, socle | C23×C821 ⋊ C4 |
| derived, Sylow | C821 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | #15692846 |
| commutator, hypocenter | C821 | C23×C4 |
| Frattini | C1 | G |
| Fitting, socle | C23×C821 | C4 |
| prime radical | C23×D821 | C2 |
| cosocle | D821 | C24 |
| LCS | G ▷ C821 | |
| UCS | C1 ◁ C23 | |
236 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6568 |
1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26272, 235);