Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C3×C4×D4 ⋊ C2 |
| Sylow | C3 ⋊ #2358 |
928 conjugacy classes of subgroups.
| minimal degree | μ(G) = 15 |
| transitive degree | μt(G) = 96 |
A minimal faithful permutation representation — 4 generators on 15 points:
(1,2,3)(13,15);(2,3)(9,11);(4,6,7,5)(12,13)(14,15);(4,5,7,6)(8,9)(10,11)(13,15)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,b^a=be,c^a=cf,d^b=de,h^c=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2358, C2×#82398, #10954749, … |
| maximal normal subgroup of | D3×#2358, C2×#82398, #10954749, … |
| maximal quotient of | C22⋊C4×(C2×D3)⋊C4, #10716682, #10716684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 14974);