Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #85647 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting, Sylow | C22×#127 ⋊ C3 |
| derived | C22×C42 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22×C42 | C2×C3 |
| Frattini | C22 | C2×C22⋊A4 |
| Fitting | C22×#127 | C3 |
| socle | C24 | C2×A4 |
| LCS | G ▷ C22×C42 | |
| UCS | C1 | |
540 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 16 points:
(2,3,4)(5,6,9)(7,11,14,12,13,16)(8,10,15);(1,4)(2,3)(6,10)(9,15)(11,13)(14,16);(5,12,8,7)(6,11,10,13)(9,15)(14,16)Polycyclic presentation:
2,3,2^6|c^2=g,d^2=h,c^a=cg,d^a=dh,c^b=cdefg,d^b=cfh,e^b=efh,f^b=eg,g^b=gh,h^b=g24 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18223);