Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C11 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C22×D11 |
| commutator, socle | C2×C11 | C22×C4 |
| Fitting, prime radical | C11×#41 | C2 |
| cosocle | C4×C11 | C23 |
| hypercenter | #41 | D11 |
| hypocenter | C11 | #131 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C4 ◁ #41 | |
62 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 3 generators on 27 points:
(1,2,4,6,8,10,11,9,7,5,3)(14,20)(17,23)(21,26)(24,27);(12,14)(13,17)(15,21)(16,20)(18,24)(19,23)(22,26)(25,27);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,15,18,16,19,22,25)(14,17,21,24,20,23,26,27)Polycyclic presentation:
2^5,11|a^2=d,d^2=e,f^a=f^10,c^b=ce70 conjugacy classes — view the full character table.
| maximal subgroup of | #10622436, #10622437, #10622809, … |
| maximal normal subgroup of | #10622436, #10622437, #10622809, … |
| maximal quotient of | #10622610, #10622612, #10622613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 143);