Finite Group DatabasebetaFinite Group Databasebeta| order | 5536 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C173 ⋊ C4 |
| Sylow | C173 ⋊ #117 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×#10621924 |
| commutator, socle | C2×C173 | C22×C4 |
| Frattini | C2 | C22×#10621924 |
| Fitting | C2×C4×C173 | C4 |
| hypercenter | C2×C4 | #10621924 |
| hypocenter | C173 | #117 |
| LCS | G ▷ C2×C173 ▷ C173 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,173|a^2=e,c^2=d,b^a=bd,f^a=f^80,f^e=f^172364 conjugacy classes — view the full character table.
| maximal subgroup of | #26012358, #26012359, #26012362, … |
| maximal normal subgroup of | #26012358, #26012359, #26012362, … |
| maximal quotient of | #26012427, C4×C22⋊#10621924, C4×C4⋊#10621924, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5536, 225);