Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C59×#443 ⋊ C2 |
| Sylow | C59 ⋊ #3292 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D236 |
| commutator | C2×C4×C59 | C24 |
| Frattini | C2×C4 | C23×D59 |
| Fitting | C59×#443 | C2 |
| socle | C2×C59 | D42 |
| hypercenter | #443 | D59 |
| hypocenter | C59 | #3292 |
| LCS | G ▷ C2×C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ #443 | |
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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=g,e^2=g,f^2=g,b^a=be,c^a=cf,e^a=eg,f^a=fg,h^a=h^58,c^b=cg,d^b=de,e^b=eg,f^c=fg,h^c=h^58,e^d=eg841 conjugacy classes — view the full character table.
| maximal subgroup of | #28502081, #28502084, #28502091, … |
| maximal normal subgroup of | #28502081, #28502084, #28502091, … |
| maximal quotient of | #28579977, #28579978, #28580080, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 16310);