Finite Group DatabasebetaFinite Group Databasebeta| order | 384 |
| isoclinism | isoclinic class of #1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C23 |
No aliases for this group.
| derived | C22⋊A4 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #1020 |
| commutator, hypocenter | C22⋊A4 | C8 |
| Fitting | C24×C4 | D3 |
| socle | C25 | Dic3 |
| prime radical | C2×C22⋊A4 | C4 |
| cosocle | C4×C22⋊A4 | C2 |
| LCS | G ▷ C22⋊A4 | |
| UCS | C1 ◁ C4 | |
229 conjugacy classes of subgroups.
| minimal degree | μ(G) = 16 |
| transitive degree | μt(G) = 24 |
A minimal faithful permutation representation — 2 generators on 16 points:
(1,2,4,3)(5,6,8,7)(9,10,11,13,12,14,15,16);(2,3,4)(6,8,7)Polycyclic presentation:
2^3,3,2^4|a^2=b,b^2=c,d^a=d^2,e^a=f,f^a=e,g^a=h,h^a=g,e^d=f,f^d=ef,g^d=gh,h^d=g40 conjugacy classes — view the full character table.
| maximal subgroup of | #1020⋊C8, #11711113, #11711114, … |
| maximal normal subgroup of | #1020⋊C8, #11711113, #11711114, … |
| maximal quotient of | #11714224, #11714225, #11714226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(384, 18137);