Finite Group DatabasebetaFinite Group Databasebeta| order | 36928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#32914660 |
| Fitting | C22×D4×C577 ⋊ C2 |
| Sylow | C577 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D577 |
| commutator, cosocle | C22×C577 | C24 |
| Frattini | C22 | C23×D577 |
| Fitting | C22×D4×C577 | C2 |
| socle | C23×C577 | C23 |
| hypercenter | C22×D4 | D577 |
| hypocenter | C577 | C2×#127 |
| LCS | G ▷ C22×C577 ▷ C577 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18464 |
5788 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36928, 1088);