Finite Group DatabasebetaFinite Group Databasebeta| order | 272 |
| isoclinism | isoclinic class of #63228 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C17 ⋊ SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D17 |
| commutator, cosocle | C4×C17 | C22 |
| Frattini | C4 | C2×D17 |
| Fitting, prime radical | D4×C17 | C2 |
| socle | C2×C17 | D4 |
| hypercenter | D4 | D17 |
| hypocenter | C17 | SD16 |
| LCS | G ▷ C4×C17 ▷ C2×C17 ▷ C17 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 136 |
A minimal faithful permutation representation — 2 generators on 25 points:
(1,2,4,6,8,10,12,14,16,17,15,13,11,9,7,5,3)(19,22)(20,25)(23,24);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19,21,24)(20,22,25,23)Polycyclic presentation:
2^4,17|a^2=d,c^2=d,b^a=bc,c^a=cd,e^a=e^16,c^b=cd47 conjugacy classes — view the full character table.
| maximal subgroup of | #10587597, #10587598, SD16×D17, … |
| maximal normal subgroup of | #10587597, #10587598, SD16×D17, … |
| maximal quotient of | #10587479, #10587481, #10587503, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(272, 16);