Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
122 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 122 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) = 48 |
| transitive degree | μt(G) = 48 |
A minimal faithful permutation representation — 2 generators on 48 points:
(1,37,41,14,17,47,5,34,35,3,6,46,8,31,20,18,19,32,4,15,38,16,23,39)(2,30,40,13,27,44,10,24,36,9,29,48,12,42,21,26,22,45,7,43,28,25,11,33);(1,2,5,10,8,12,4,7)(3,13,14,25,16,26,18,9)(6,20,19,38,23,41,17,35)(11,28,27,40,29,36,22,21)(15,32,31,46,34,47,37,39)(24,33,30,45,43,48,42,44)Polycyclic presentation:
2^4,3,2^3|a^2=d,b^2=c,c^2=h,d^2=h,f^2=h,g^2=h,b^a=bd,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×#73129, #11712689, #11712836, … |
| maximal normal subgroup of | C2×#73129, #11712689, #11712836, … |
| maximal quotient of | #11711083, #11711084, #11711100, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5705);