Finite Group DatabasebetaFinite Group Databasebeta| order | 320 |
| isoclinism | isoclinic class of (C24⋊C5)⋊C2 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| derived | C24⋊C5 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | (C24⋊C5)⋊C2 |
| commutator, hypocenter | C24⋊C5 | C4 |
| Fitting, socle | C25 | D5 |
| prime radical, cosocle | C2×C24⋊C5 | C2 |
| LCS | G ▷ C24⋊C5 | |
| UCS | C1 ◁ C2 | |
111 conjugacy classes of subgroups.
| minimal degree | μ(G) = 14 |
| transitive degree | μt(G) = 20 |
A minimal faithful permutation representation — 2 generators on 14 points:
(1,2,3,4)(6,8,10,11)(9,14,13,12);(5,6,9,12,8)(7,10,13,14,11)Polycyclic presentation:
2^2,5,2^4|a^2=b,c^a=c^4,d^a=de,f^a=deg,g^a=df,d^c=de,e^c=ef,f^c=fg,g^c=d20 conjugacy classes — view the full character table.
| maximal subgroup of | #10619374, (C24⋊C5)⋊Q8, C4×(C24⋊C5)⋊C2, … |
| maximal normal subgroup of | #10619374, (C24⋊C5)⋊Q8, C4×(C24⋊C5)⋊C2, … |
| maximal quotient of | #10617015, #10617016, #10617017, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(320, 1583);