Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×C17 ⋊ C2 |
| Sylow | C17 ⋊ #135 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D4×D17 |
| commutator, cosocle | C4×C17 | C23 |
| Frattini | C4 | C22×D17 |
| Fitting | SD16×C17 | C2 |
| socle | C2×C17 | C2×D4 |
| hypercenter | SD16 | D17 |
| hypocenter | C17 | #135 |
| LCS | G ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ SD16 | |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^5,17|c^2=e,d^2=e,b^a=be,c^a=ce,f^a=f^16,c^b=cd,d^b=de,d^c=de70 conjugacy classes — view the full character table.
| maximal subgroup of | #135×D17, C2×#10587602, #11763605, … |
| maximal normal subgroup of | #135×D17, C2×#10587602, #11763605, … |
| maximal quotient of | #11762802, #11762804, #11762844, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 138);