Finite Group DatabasebetaFinite Group Databasebeta| order | 26272 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#27190149 |
| Fitting | C22×C4×C821 ⋊ C2 |
| Sylow | C821 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D821 |
| commutator, cosocle | C2×C821 | C24 |
| Frattini | C2 | C23×D821 |
| Fitting | C22×C4×C821 | C2 |
| socle | C22×C821 | C23 |
| hypercenter | C22×C4 | D821 |
| hypocenter | C821 | C2×#41 |
| LCS | G ▷ C2×C821 ▷ C821 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13136 |
6580 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(26272, 189);