Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#4813 |
| Fitting | C2×C3×#103 ⋊ C2 |
| Sylow | C3 ⋊ C2×#467 |
512 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 192 |
A minimal faithful permutation representation — 4 generators on 25 points:
(3,4,5)(6,7)(8,9)(10,13,15,12)(11,16,18,20)(14,19,21,22)(17,24,25,23);(7,9)(10,12,14,19,15,13,21,22)(11,16,17,23,18,20,25,24);(1,2)(4,5)(7,9)(10,11)(12,16)(13,20)(14,17)(15,18)(19,23)(21,25)(22,24);(1,2)72 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#4813, #10801693, #10801729, … |
| maximal normal subgroup of | C4×#4813, #10801693, #10801729, … |
| maximal quotient of | C2×#68441, C2×#68497, C2×#68447, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 11373);