Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #519 ⋊ D3 |
162 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 162 conjugacy classes of subgroups — too many to draw. Only its 24 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,27,19,3,17,30)(2,25,23,11,18,32,8,21,24,7,9,31)(4,29,6,13,16,12)(5,14)(10,22,15,26)(20,28);(1,2)(3,11)(4,15)(5,18)(6,8)(7,12)(9,20)(10,17)(13,22)(14,21)(16,24)(19,23)(25,28)(26,27)(29,31)(30,32)Polycyclic presentation:
2^4,3,2^3|b^2=c,f^2=h,g^2=h,b^a=bd,c^a=ch,e^a=e^2,f^a=gh,g^a=fh,d^b=dh,f^e=g,g^e=fgh,g^f=gh31 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73074, #11712761, #11712946, … |
| maximal normal subgroup of | C2×#73074, #11712761, #11712946, … |
| maximal quotient of | #11711148, #11711149, #11711168, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5650);