Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #519 ⋊ D3 |
259 conjugacy classes of subgroups; only the 38 normal subgroups are shown.
This group has 259 conjugacy classes of subgroups — too many to draw. Only its 38 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 36 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 3 generators on 36 points:
(1,2,3,4)(5,19,24)(6,13,28,12,23,27)(7,17,34,16,31,33)(8,9,22)(11,29,36)(14,21)(15,25,35)(18,32);(5,7)(6,11)(8,16)(9,17)(10,18)(12,15)(13,25)(14,26)(19,31)(20,32)(21,30)(22,33)(23,29)(24,34)(27,35)(28,36);(2,4)(5,6)(7,15)(8,12)(9,21)(10,23)(11,16)(13,20)(14,19)(17,26)(18,25)(22,28)(24,27)(29,32)(30,31)(33,35)(34,36)Polycyclic presentation:
2^4,3,2^3|c^2=dh,f^2=h,g^2=h,b^a=bh,c^a=cd,e^a=e^2,f^a=gh,g^a=fh,c^b=ch,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | #11713365, C2×#85359, #11714741, … |
| maximal normal subgroup of | #11713365, C2×#85359, #11714741, … |
| maximal quotient of | #11712226, #11712227, #11712228, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 17935);