Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C4⋊C8 ⋊ C2 |
| Sylow | C3 ⋊ #2990 |
398 conjugacy classes of subgroups.
| minimal degree | μ(G) = 19 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 19 points:
(1,2,3)(4,6,7,10)(5,9,8,11)(12,14,15,16)(13,18,17,19);(5,8)(9,11);(2,3)(4,5)(6,9)(7,8)(10,11)(13,17)(18,19);(5,8)(6,10)(12,13,16,18,15,17,14,19)Polycyclic presentation:
2^7,3|a^2=f,d^2=e,f^2=g,b^a=be,d^a=de,c^b=ceg,h^b=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | #10762153, #10762156, #10762171, … |
| maximal normal subgroup of | #10762153, #10762156, #10762171, … |
| maximal quotient of | #10793999, #10794000, #10794024, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11591);