Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C26×C42 |
| direct product | H(3,𝔽4)×D59 |
| Fitting | C59×H(3,𝔽4) ⋊ C2 |
| Sylow | C59 ⋊ C2×H(3,𝔽4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C24×D59 |
| commutator, socle | C22×C59 | C25 |
| Fitting | C59×H(3,𝔽4) | C2 |
| hypercenter | H(3,𝔽4) | D59 |
| hypocenter | C59 | C2×H(3,𝔽4) |
| LCS | G ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ H(3,𝔽4) | |
1408 conjugacy classes of subgroups; only the 459 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 459 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
589 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1655, D59×#1659, #28569902, … |
| maximal normal subgroup of | D59×#1655, D59×#1659, #28569902, … |
| maximal quotient of | D59×#2375, D59×#2379, #28751391, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 18629);