Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of D48 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#4503 |
| Sylow | C3 ⋊ C2×#358 |
232 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 101 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) = 384 |
A minimal faithful permutation representation — 3 generators on 25 points:
(3,4,5)(7,9)(10,11,16,25,14,18,12,15,13,17,19,24,20,22,21,23);(4,5)(6,7,8,9)(11,15)(12,19)(14,20)(16,21)(17,23)(18,25)(22,24);(1,2)108 conjugacy classes — view the full character table.
| maximal subgroup of | #10710395, C4×#4503, #10710405, … |
| maximal normal subgroup of | #10710395, C4×#4503, #10710405, … |
| maximal quotient of | C2×#67505, #10705167, #10705219, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 3991);