Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#5698 |
| Fitting | C2×C3×#125 ⋊ C2 |
| Sylow | C3 ⋊ C2×#541 |
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2)(3,4,5)(6,8,9,13)(7,11,10,12)(14,17)(15,21)(16,23)(18,25)(19,26)(20,24)(22,28)(27,29);(6,7,9,10)(8,12,13,11)(15,20)(16,22)(17,25)(26,29);(14,16,18,22)(15,19,20,27)(17,23,25,28)(21,26,24,29);(4,5)(7,10)(11,12)(14,15)(16,19)(17,24)(18,20)(21,25)(22,27)(23,29)(26,28);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | #10687726, #10800344, #10800470, … |
| maximal normal subgroup of | #10687726, #10800344, #10800470, … |
| maximal quotient of | C2×#74224, C2×#75970, C2×#76197, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18669);