Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#63256 |
| Fitting | C2×Q8×C17 ⋊ C2 |
| Sylow | C17 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D17 |
| commutator, cosocle | C2×C17 | C24 |
| Frattini | C2 | C23×D17 |
| Fitting | C2×Q8×C17 | C2 |
| socle | C22×C17 | C23 |
| hypercenter | C2×Q8 | D17 |
| hypocenter | C17 | C2×#41 |
| LCS | G ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
100 conjugacy classes — view the full character table.
| maximal subgroup of | #11762792, #11762804, #11762809, … |
| maximal normal subgroup of | #11762792, #11762804, #11762809, … |
| maximal quotient of | C2×#10587578, C2×#10587579, C2×Q8×Dic17, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 229);