Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C3×C4×C4⋊C4 ⋊ C2 |
| Sylow | C3 ⋊ #2362 |
576 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)(12,15,16,14)(13,18,17,19);(9,11)(12,14,16,15)(13,18,17,19);(4,6,7,5)(12,13)(14,18)(15,19)(16,17);(2,3)(4,5,7,6)(8,9)(10,11)(13,17)(18,19)Polycyclic presentation:
2^7,3|a^2=g,b^2=g,c^2=e,d^2=e,b^a=be,c^a=cf,h^a=h^2,d^b=de,h^d=h^290 conjugacy classes — view the full character table.
| maximal subgroup of | D3×#2362, C2×#73648, #10954750, … |
| maximal normal subgroup of | D3×#2362, C2×#73648, #10954750, … |
| maximal quotient of | #10716613, #10716704, #10716707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 6224);