Finite Group DatabasebetaFinite Group Databasebeta| order | 19375 |
| automorphism | ? |
| homology | Abelianization (H1) = C53 · Schur multiplier (H2) = C54 |
| direct product | H(3,𝔽5)×ΓL(1,𝔽32) |
| Fitting | C31×H(3,𝔽5) ⋊ C5 |
| Sylow | C31 ⋊ C5×H(3,𝔽5) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C5 | C52×ΓL(1,𝔽32) |
| commutator, socle, cosocle | C5×C31 | C53 |
| Fitting | C31×H(3,𝔽5) | C5 |
| hypercenter | H(3,𝔽5) | ΓL(1,𝔽32) |
| hypocenter | C31 | C5×H(3,𝔽5) |
| LCS | G ▷ C5×C31 ▷ C31 | |
| UCS | C1 ◁ C5 ◁ H(3,𝔽5) | |
260 conjugacy classes of subgroups.
| transitive degree | μt(G) = 775 |
319 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19375, 48);