Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #4656 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×C3×C4×Q8 ⋊ C2 |
| Sylow | C3 ⋊ #2396 |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 23 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 23 points:
(1,2,3)(16,18,19,22)(17,21,20,23);(5,7)(8,10,11,15)(9,12,13,14);(2,3)(4,5)(6,7)(17,20)(21,23);(8,9,11,13)(10,14,15,12)(16,17)(18,21)(19,20)(22,23)Polycyclic presentation:
2^7,3|a^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,c^b=cg,h^b=h^284 conjugacy classes — view the full character table.
| maximal subgroup of | #10690273, #10690278, #10767462, … |
| maximal normal subgroup of | #10690273, #10690278, #10767462, … |
| maximal quotient of | #10716898, #10716912, #10716934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 15067);