Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| isoclinism | isoclinic class of #66890 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C11 ⋊ Q32 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #4323 |
| commutator, cosocle | C8×C11 | C22 |
| Frattini | C8 | C2×D11 |
| Fitting | C11×Q16 | C2 |
| socle, prime radical | C2×C11 | D8 |
| hypercenter | Q16 | D11 |
| hypocenter | C11 | Q32 |
| LCS | G ▷ C8×C11 ▷ C4×C11 ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ Q16 | |
24 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,4,6,8,10,11,9,7,5,3)(12,14,17,25)(13,18,21,35)(15,27,30,43)(16,32,28,24)(19,37,38,42)(20,39,31,34)(22,40,41,26)(23,36,33,29);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,17,21)(14,22,25,41)(15,26,30,40)(16,31,28,20)(18,33,35,23)(19,36,38,29)(24,42,32,37)(27,39,43,34)Polycyclic presentation:
2^5,11|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^10,c^b=cd,d^b=de46 conjugacy classes — view the full character table.
| maximal subgroup of | #10622528, #10622529, D11×Q32, … |
| maximal normal subgroup of | #10622528, #10622529, D11×Q32, … |
| maximal quotient of | #10622127, #10622130, #10622202, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 35);