Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C59×#497 ⋊ C2 |
| Sylow | C59 ⋊ #3153 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#497 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #497 | D59 |
| hypocenter | C59 | #3153 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #497 | |
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,59|b^2=e,c^2=fg,e^2=g,b^a=be,c^a=cf,e^a=eg,d^b=dg,h^c=h^58,h^d=h^58496 conjugacy classes — view the full character table.
| maximal subgroup of | #28508981, #28569906, #28569914, … |
| maximal normal subgroup of | #28508981, #28569906, #28569914, … |
| maximal quotient of | #28576549, #28576564, #28576593, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 14973);