Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| isoclinism | isoclinic class of #3633 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C17 ⋊ C2×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #3633 |
| commutator, hypocenter | C17 | C2×C16 |
| Frattini | C2 | C2×#3633 |
| Fitting | C4×C17 | C8 |
| socle | C2×C17 | C2×C8 |
| prime radical | C2×D17 | C8 |
| cosocle | #3624 | C22 |
| LCS | G ▷ C17 | |
| UCS | C1 ◁ C4 | |
28 conjugacy classes of subgroups.
| transitive degree | μt(G) = 272 |
Polycyclic presentation:
2^5,17|a^2=c,b^2=e,c^2=d,d^2=e,f^a=f^9,f^c=f^13,f^d=f^1640 conjugacy classes — view the full character table.
| maximal subgroup of | #11763902, #11763904, #11763909, … |
| maximal normal subgroup of | #11763902, #11763904, #11763909, … |
| maximal quotient of | C4×#63241, #11763906, #11763912, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 201);