Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#3633 |
| Fitting | C4×C17 ⋊ C8 |
| Sylow | C17 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#3633 |
| commutator, socle | C2×C17 | C2×C8 |
| Fitting | C4×C17 | C8 |
| prime radical | C2×D17 | C2×C4 |
| cosocle | C2×#595 | C22 |
| hypercenter | C4 | #3633 |
| hypocenter | C17 | C4⋊C8 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C4 | |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 68 |
Polycyclic presentation:
2^5,17|a^2=c,b^2=d,c^2=e,b^a=bd,f^a=f^9,f^c=f^13,f^e=f^1628 conjugacy classes — view the full character table.
| maximal subgroup of | D4⋊#3633, Q8⋊#3633, #11763898, … |
| maximal normal subgroup of | D4⋊#3633, Q8⋊#3633, #11763898, … |
| maximal quotient of | #11763898, #11763899, (C2×#3633)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 204);