Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C173 ⋊ C2 |
| Sylow | C173 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center | C8 | C2×D173 |
| commutator, socle | C2×C173 | C22×C4 |
| Frattini | C4 | C22×D173 |
| Fitting | C2×C8×C173 | C2 |
| hypercenter | C2×C8 | D173 |
| hypocenter | C173 | #131 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C8 ◁ C2×C8 | |
62 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=d,d^2=e,c^b=ce,f^c=f^1721396 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #26011274, #26011276, #26011606, … |
| maximal normal subgroup of | #26011274, #26011276, #26011606, … |
| maximal quotient of | #26011445, #26011446, #26011456, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 152);