Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #5386 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#226 |
275 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 275 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 3 generators on 22 points:
(3,4,5,6)(7,9,16)(8,12,20)(11,17,18)(14,21,22);(4,6)(7,8,11,14)(9,13,17,19)(10,12,15,21)(16,22,18,20);(1,2)46 conjugacy classes — view the full character table.
| maximal subgroup of | #11711121, #11711181, #11711194, … |
| maximal normal subgroup of | #11711121, #11711181, #11711194, … |
| maximal quotient of | C2×#73012, C2×#73013, C2×#73014, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17896);