Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C17 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#595 |
| commutator, socle | C2×C17 | C22×C4 |
| Fitting | Q8×C17 | C4 |
| prime radical | #63256 | C2 |
| cosocle | Dic17 | C23 |
| hypercenter | Q8 | #595 |
| hypocenter | C17 | #131 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^5,17|a^2=d,b^2=e,c^2=e,d^2=e,f^a=f^13,c^b=ce,f^d=f^1640 conjugacy classes — view the full character table.
| maximal subgroup of | #11763852, #11763853, #11763854, … |
| maximal normal subgroup of | #11763852, #11763853, #11763854, … |
| maximal quotient of | #11763774, #11763784, #11763816, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 216);