Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#492 ⋊ C2 |
| Sylow | C59 ⋊ #3291 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #16838037 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#492 | C2 |
| socle | C2×C59 | D42 |
| hypercenter | #492 | D59 |
| hypocenter | C59 | #3291 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #492 | |
460 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 117 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,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,c^b=cg,d^b=de,e^b=eg,h^b=h^58,f^c=fg,h^c=h^58,e^d=eg,h^d=h^58667 conjugacy classes — view the full character table.
| maximal subgroup of | #28502100, #28502103, #28502105, … |
| maximal normal subgroup of | #28502100, #28502103, #28502105, … |
| maximal quotient of | #28579965, #28580011, #28580032, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16303);