Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D103 |
| Fitting | H(5,𝔽2)×C103 ⋊ C2 |
| Sylow | C103 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D103 |
| commutator, socle | C2×C103 | C25 |
| Fitting | H(5,𝔽2)×C103 | C2 |
| hypercenter | H(5,𝔽2) | D103 |
| hypocenter | C103 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
901 conjugacy classes — view the full character table.
| maximal subgroup of | #453×D103, #455×D103, #27204498, … |
| maximal normal subgroup of | #453×D103, #455×D103, #27204498, … |
| maximal quotient of | #518×D103, #520×D103, #27208348, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 1378);