Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×#41 ⋊ D3 |
161 conjugacy classes of subgroups; only the 24 normal subgroups are shown.
This group has 161 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) = 32 |
| transitive degree | μt(G) = 32 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,17,19)(2,23,25,9,18,32,8,21,26,7,10,31)(3,28,29)(4,16,6)(11,22,15,24)(12,27,14);(1,2)(3,7)(4,15)(5,18)(6,8)(9,14)(10,20)(11,17)(12,24)(13,23)(16,26)(19,25)(21,30)(22,28)(27,32)(29,31)Polycyclic presentation:
2^4,3,2^3|b^2=c,d^2=h,f^2=h,g^2=h,b^a=bd,c^a=ch,d^a=dh,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×#73073, #11712763, #11712869, … |
| maximal normal subgroup of | C2×#73073, #11712763, #11712869, … |
| maximal quotient of | #11711150, #11711151, #11711166, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5649);