Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D17 |
| commutator, socle, cosocle | C2×C17 | C24 |
| Fitting | C2×Q8×C17 | C2 |
| hypercenter | C2×Q8 | D17 |
| hypocenter | C17 | 2−1+4 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^5,17|b^2=e,c^2=e,d^a=de,f^a=f^16,c^b=ce97 conjugacy classes — view the full character table.
| maximal subgroup of | #11762981, #11762984, #11762991, … |
| maximal normal subgroup of | #11762981, #11762984, #11762991, … |
| maximal quotient of | #11763285, #11763287, #11763290, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 230);