Finite Group DatabasebetaFinite Group Databasebeta| order | 26272 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×D821⋊C8 |
| unambiguous semidirect product | D821⋊(C2×C8) |
| derived, Sylow | C821 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #15692846 |
| commutator, hypocenter | C821 | C22×C8 |
| Frattini | C2 | C22×#15692846 |
| Fitting | C2×C4×C821 | C4 |
| socle | C22×C821 | C2×C4 |
| prime radical | C22×D821 | C4 |
| cosocle | Dic821 | C23 |
| LCS | G ▷ C821 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13136 |
1672 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26272, 229);