Finite Group DatabasebetaFinite Group Databasebeta| order | 352 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C11×#41 ⋊ C2 |
| Sylow | C11 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D11 |
| commutator, socle, cosocle | C2×C11 | C24 |
| Fitting | C11×#41 | C2 |
| hypercenter | #41 | D11 |
| hypocenter | C11 | 2−1+4 |
| LCS | G ▷ C2×C11 ▷ C11 | |
| UCS | C1 ◁ C2 ◁ #41 | |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 4 generators on 27 points:
(1,2,4,6,8,10,11,9,7,5,3)(12,16,17,15)(13,19,20,24)(14,21,22,23)(18,26,27,25);(12,15,17,16)(13,19,20,24)(14,21,22,23)(18,25,27,26);(12,14,17,22)(13,18,20,27)(15,23,16,21)(19,26,24,25);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,18)(15,19)(16,24)(17,20)(21,25)(22,27)(23,26)Polycyclic presentation:
2^5,11|b^2=e,c^2=e,d^2=e,d^a=de,f^a=f^10,c^b=ce67 conjugacy classes — view the full character table.
| maximal subgroup of | #10622439, #10622440, #10622814, … |
| maximal normal subgroup of | #10622439, #10622440, #10622814, … |
| maximal quotient of | #10623047, #10623049, #10623050, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(352, 185);