Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
190 conjugacy classes of subgroups; only the 28 normal subgroups are shown.
This group has 190 conjugacy classes of subgroups — too many to draw. Only its 28 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:
(1,10,19,3,18,26)(2,5,28,7,13,17)(4,21,30,9,27,31)(6,14)(8,15,32,12,23,29)(11,20)(16,24)(22,25);(1,2,4,8,7,3,12,9)(5,14,15,24,18,11,27,22)(6,13,16,23,20,10,25,21)(17,28,29,32,19,26,30,31)Polycyclic presentation:
2^4,3,2^3|a^2=c,c^2=h,d^2=h,f^2=h,g^2=h,b^a=bd,d^a=dh,e^a=e^2,f^a=gh,g^a=fh,d^b=dh,f^e=g,g^e=fgh,g^f=gh34 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#73157, #11712623, #11712836, … |
| maximal normal subgroup of | C2×#73157, #11712623, #11712836, … |
| maximal quotient of | #11711015, #11711016, #11711037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5733);