Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C59 ⋊ #1649 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | #14273695 |
| commutator | C42×C59 | C23 |
| Frattini | C42 | C22×D59 |
| Fitting | C59×#474 | C2 |
| socle | C22×C59 | #120 |
| hypercenter | #474 | D59 |
| hypocenter | C59 | #1649 |
| LCS | G ▷ C42×C59 ▷ C22×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #474 | |
234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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=g,b^2=g,c^2=g,d^2=f,e^2=g,b^a=bd,c^a=ce,d^a=df,e^a=eg,d^b=df,e^b=eg,h^b=h^58,d^c=dg,e^c=eg,h^c=h^58577 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#1649, C2×#21423344, #28564528, … |
| maximal normal subgroup of | D59×#1649, C2×#21423344, #28564528, … |
| maximal quotient of | #28477509, #28477516, #28477551, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 3758);