Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #41×C173 ⋊ C2 |
| Sylow | C173 ⋊ H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D173 |
| commutator, socle | C2×C173 | C24 |
| Fitting | #41×C173 | C2 |
| hypercenter | #41 | D173 |
| hypocenter | C173 | H(5,𝔽2) |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C2 ◁ #41 | |
166 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|b^a=be,d^a=de,c^b=ce,f^c=f^172,f^d=f^172877 conjugacy classes — view the full character table.
| maximal subgroup of | #26011657, #26011660, #26011667, … |
| maximal normal subgroup of | #26011657, #26011660, #26011667, … |
| maximal quotient of | #26011963, #26011965, #26011971, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 192);