Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #87588 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting, socle | C26 ⋊ D3 |
| derived | C22⋊(C22⋊A4) ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C22⋊(C22⋊A4) | C2 |
| Fitting, socle | C26 | D3 |
| LCS | G ▷ C22⋊(C22⋊A4) | |
| UCS | C1 | |
830 conjugacy classes of subgroups.
| minimal degree | μ(G) = 12 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 3 generators on 12 points:
(3,4)(5,7)(9,12,11,10);(2,3,4)(6,7,8)(10,11,12);(1,4)(2,3)Polycyclic presentation:
2,3,2^6|b^a=b^2,d^a=cd,e^a=ef,g^a=gh,c^b=d,d^b=cd,e^b=f,f^b=ef,g^b=h,h^b=gh24 conjugacy classes — view the full character table.
| maximal subgroup of | #87588⋊C2, C2×#87588, #10596779⋊C2, … |
| maximal normal subgroup of | #87588⋊C2, C2×#87588, #87588⋊C3, … |
| maximal quotient of | #11715843, #11715844, #11715845, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 20164);