Finite Group DatabasebetaFinite Group Databasebeta| order | 7552 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C59×M64 ⋊ C2 |
| Sylow | C59 ⋊ #1400 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | (C2×D59)⋊C4 |
| commutator | C22×C59 | C2×C16 |
| Frattini | C2×C16 | C2×D59 |
| Fitting | C59×M64 | C2 |
| socle | C2×C59 | C22⋊C16 |
| hypercenter | M64 | D59 |
| hypocenter | C59 | #1400 |
| LCS | G ▷ C22×C59 ▷ C2×C59 ▷ C59 | |
| UCS | C1 ◁ C8 ◁ C2×C16 ◁ M64 | |
74 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,59|a^2=d,d^2=e,e^2=f,f^2=g,b^a=bc,c^a=cg,d^b=dg,h^b=h^581204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D59×#1400, C2×#21422235, #28508891, … |
| maximal normal subgroup of | D59×#1400, C2×#21422235, #28508891, … |
| maximal quotient of | #28476027, #28476087, #28476129, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7552, 2649);