Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C2×H(5,𝔽2)×D59 |
| Fitting | C2×H(5,𝔽2)×C59 ⋊ C2 |
| Sylow | C59 ⋊ C22×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C24×D59 |
| commutator | C2×C59 | C26 |
| Frattini | C2 | C25×D59 |
| Fitting | C2×H(5,𝔽2)×C59 | C2 |
| socle | C22×C59 | C25 |
| hypercenter | C2×H(5,𝔽2) | D59 |
| hypocenter | C59 | C22×H(5,𝔽2) |
| LCS | G ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C2×H(5,𝔽2) | |
6560 conjugacy classes of subgroups; only the 3213 normal subgroups are shown.
This group has 6560 conjugacy classes of subgroups — too many to draw. Only its 3213 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1054 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1790, #28587954, D59×#1792, … |
| maximal normal subgroup of | D59×#1790, #28587954, D59×#1792, … |
| maximal quotient of | C2×#518×D59, C2×#520×D59, C4×H(5,𝔽2)×D59, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 19310);