Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C59×#461 ⋊ C2 |
| Sylow | C59 ⋊ #3298 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D4×D59 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#461 | C2 |
| socle | C22×C59 | C22×D4 |
| hypercenter | #461 | D59 |
| hypocenter | C59 | #3298 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #461 | |
420 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 123 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=e,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^58,d^b=de,h^b=h^58,f^c=fg,h^c=h^58,h^d=h^58586 conjugacy classes — view the full character table.
| maximal subgroup of | #28578194, #28578198, #28578209, … |
| maximal normal subgroup of | #28578194, #28578198, #28578209, … |
| maximal quotient of | #28604124, #28604900, #28605836, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16378);