Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C59 ⋊ #1659 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273696 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×H(3,𝔽4) | C2 |
| socle | C22×C59 | #120 |
| hypercenter | H(3,𝔽4) | D59 |
| hypocenter | C59 | #1659 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ H(3,𝔽4) | |
228 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|a^2=f,d^2=f,e^2=fg,b^a=bd,c^a=ce,d^a=df,e^a=efg,h^a=h^58,d^b=df,e^b=eg,d^c=dg,e^c=efg571 conjugacy classes — view the full character table.
| maximal subgroup of | #28509425, #28509426, D59×#1659, … |
| maximal normal subgroup of | #28509425, #28509426, D59×#1659, … |
| maximal quotient of | #28477476, #28477505, #28477522, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3816);