Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
156 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 26 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) = 128 |
A minimal faithful permutation representation — 2 generators on 36 points:
(1,3,4,2)(5,27,34,11,8,26,15,22,21,6,31,36,10,12,33,24,20,29,7,28,19,14,16,35)(9,13,17,23,18,30,32,25);(1,2,4,3)(6,11)(7,15)(8,18)(9,20)(12,25)(13,28)(14,24)(16,17)(19,21)(22,30)(23,27)(26,36)(29,35)(31,32)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=cd,c^2=h,f^2=h,g^2=h,b^a=bc,c^a=ch,e^a=e^2,f^a=gh,g^a=fh,f^e=g,g^e=fgh,g^f=gh40 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73124, #11712766, #11712767, … |
| maximal normal subgroup of | C2×#73124, #11712766, #11712767, … |
| maximal quotient of | #11711151, #11711169, #11711171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5700);