Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C2×C32×C59 ⋊ C2 |
| Sylow | C59 ⋊ #1401 |
| subgroup | G/H | |
|---|---|---|
| center | C16 | D236 |
| commutator | C4×C59 | C2×C16 |
| Frattini | C2×C16 | C2×D59 |
| Fitting | C2×C32×C59 | C2 |
| socle | C2×C59 | C22⋊C16 |
| hypercenter | C2×C32 | D59 |
| hypocenter | C59 | #1401 |
| LCS | G ▷ C4×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C16 ◁ C2×C16 ◁ C2×C32 | |
72 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,c^2=g,d^2=e,e^2=f,f^2=g,b^a=bc,c^b=cg,d^b=dg,h^b=h^581912 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1401, C2×#21422237, #28508898, … |
| maximal normal subgroup of | D59×#1401, C2×#21422237, #28508898, … |
| maximal quotient of | #28476029, #28476089, #28476128, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2651);