Finite Group DatabasebetaFinite Group Databasebeta| order | 288 |
| isoclinism | isoclinic class of #63734 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C32 ⋊ Q32 |
42 conjugacy classes of subgroups.
| minimal degree | μ(G) = 38 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 2 generators on 38 points:
(1,3)(2,5,6)(7,9,12,20)(8,13,16,30)(10,22,25,38)(11,27,23,19)(14,32,33,37)(15,34,26,29)(17,35,36,21)(18,31,28,24);(1,2)(3,6)(4,5)(7,8,12,16)(9,17,20,36)(10,21,25,35)(11,26,23,15)(13,28,30,18)(14,31,33,24)(19,37,27,32)(22,34,38,29)Polycyclic presentation:
2^5,3^2|a^2=e,b^2=e,c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,f^a=f^2,c^b=cd,d^b=de,f^b=g,g^b=f,f^c=f^2,g^c=g^221 conjugacy classes — view the full character table.
| maximal subgroup of | #10593275, #10593279, #10593280, … |
| maximal normal subgroup of | #10593275, #10593279, #10593280, … |
| maximal quotient of | #10590062, #10590068, C2×#63736, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(288, 384);