Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #3358⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | #3395⋊C3 |
| Fitting, Sylow | #3395 ⋊ C3 |
103 conjugacy classes of subgroups.
| minimal degree | μ(G) = 32 |
| transitive degree | μt(G) = 128 |
A minimal faithful permutation representation — 2 generators on 32 points:
(1,3,5,11)(2,6,8,15)(4,13,14,10)(7,16,12,9)(17,19,22,18)(20,32,21,23,27,24,29,31,30,25,28,26);(1,2,5,8)(3,9,11,16)(4,12,14,7)(6,13,15,10)(17,32)(18,27)(19,28)(20,26)(21,23)(22,31)(24,29)(25,30)Polycyclic presentation:
2^2,3,2^5|a^2=eh,b^2=eh,d^2=e,f^2=h,g^2=h,b^a=bd,d^a=de,d^b=de,f^c=fgh,g^c=fh,g^f=gh49 conjugacy classes — view the full character table.
| maximal subgroup of | #33926⋊C3, #33930⋊C3, #33959⋊C3, … |
| maximal normal subgroup of | #33926⋊C3, #33930⋊C3, #33959⋊C3, … |
| maximal quotient of | #22542⋊C3, SL(2,𝔽3)×#107, C2×#3395⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 5848);