Finite Group DatabasebetaFinite Group Databasebeta| order | 27008 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C32 · Schur multiplier (H2) = C4 |
| direct product | C32×Dic211 |
| derived, Sylow | C211 ⋊ C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D211 |
| commutator, hypocenter | C211 | C4×C32 |
| Frattini | C2×C16 | C2×D211 |
| Fitting | C2×C32×C211 | C2 |
| socle, prime radical | C22×C211 | C2×C16 |
| cosocle | C2×C16×C211 | C22 |
| LCS | G ▷ C211 | |
| UCS | C1 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 27008 |
6848 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27008, 2641);