Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#5409 |
363 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 363 conjugacy classes of subgroups — too many to draw. Only its 68 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 3 generators on 14 points:
(1,2)(3,4,6)(8,11)(12,14);(4,5)(7,8,9,12,10,11,13,14);(1,2)56 conjugacy classes — view the full character table.
| maximal subgroup of | #11711287, A4⋊#338, #11711291, … |
| maximal normal subgroup of | #11711287, A4⋊#338, #11711291, … |
| maximal quotient of | C2×#73055, C2×#73069, #11711792, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18053);