Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C59×#350 ⋊ C2 |
| Sylow | C59 ⋊ #2117 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | D4×D59 |
| commutator | C4×C59 | C22×C8 |
| Frattini | C2×C8 | C22×D59 |
| Fitting | C59×#350 | C2 |
| socle | C2×C59 | C2×C22⋊C8 |
| hypercenter | #350 | D59 |
| hypocenter | C59 | #2117 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C8 ◁ C2×C8 ◁ #350 | |
220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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,d^2=g,e^2=f,f^2=g,b^a=bd,c^a=cg,d^b=dg,e^b=eg,h^c=h^58856 conjugacy classes — view the full character table.
| maximal subgroup of | D59×#2117, C2×#21425722, #28741393, … |
| maximal normal subgroup of | D59×#2117, C2×#21425722, #28741393, … |
| maximal quotient of | #28497759, #28497762, #28497831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 6136);