Finite Group DatabasebetaFinite Group Databasebeta| order | 20288 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D317 |
| Fitting | H(5,𝔽2)×C317 ⋊ C2 |
| Sylow | C317 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D317 |
| commutator, socle, cosocle | C2×C317 | C25 |
| Fitting | H(5,𝔽2)×C317 | C2 |
| hypercenter | H(5,𝔽2) | D317 |
| hypocenter | C317 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C317 ▷ C317 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2536 |
2720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20288, 1378);