Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#5753 |
| Fitting | C2×C3×#131 ⋊ C2 |
| Sylow | C3 ⋊ C2×#578 |
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 37 points:
(3,4,5)(6,10,19,32,11,24,8,18)(7,14,12,26,16,30,15,23)(9,21,20,33,22,35,17,31)(13,28,25,36,29,37,27,34);(1,2)(6,9,11,22)(7,13,16,29)(8,17,19,20)(10,21,24,35)(12,25,15,27)(14,28,30,37)(18,31,32,33)(23,34,26,36);(6,8,11,19)(7,12,16,15)(9,20,22,17)(10,18,24,32)(13,27,29,25)(14,26,30,23)(21,33,35,31)(28,34,37,36);(4,5)(6,7)(8,12)(9,13)(10,23)(11,16)(14,18)(15,19)(17,25)(20,27)(21,34)(22,29)(24,26)(28,31)(30,32)(33,37)(35,36);(1,2)84 conjugacy classes — view the full character table.
| maximal subgroup of | #10710877, #10710880, #10710887, … |
| maximal normal subgroup of | #10710877, #10710880, #10710887, … |
| maximal quotient of | C2×#83806, C2×#83785, C2×#78571, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 19740);