Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #520 ⋊ D3 |
185 conjugacy classes of subgroups; only the 26 normal subgroups are shown.
This group has 185 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) = 28 |
| transitive degree | μt(G) = 64 |
A minimal faithful permutation representation — 2 generators on 28 points:
(1,2,3,4)(5,24,28,11,16,26,7,19,21,6,18,25)(8,20,22,10,14,17,13,12,27,15,9,23);(6,10)(8,13)(9,17)(11,15)(12,21)(14,23)(16,25)(18,26)(19,22)(20,28)(24,27)Polycyclic presentation:
2^4,3,2^3|b^2=c,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×#73078, #11712736, #11712737, … |
| maximal normal subgroup of | C2×#73078, #11712736, #11712737, … |
| maximal quotient of | #11711109, #11711116, #11711118, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5654);