Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| isoclinism | isoclinic class of C13⋊#1020 |
| automorphism | ? |
| homology | Abelianization (H1) = C2 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | C13⋊#1020 |
| Fitting, socle | C24×C13 ⋊ D3 |
| derived | C13×C22⋊A4 ⋊ C2 |
| Sylow | C13 ⋊ #1020 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C13×C22⋊A4 | C2 |
| Fitting, socle | C24×C13 | D3 |
| LCS | G ▷ C13×C22⋊A4 | |
| UCS | C1 | |
112 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2,3,13,2^4|b^a=b^2,c^a=c^12,d^a=de,f^a=fg,d^b=e,e^b=de,f^b=g,g^b=fg58 conjugacy classes — view the full character table.
| maximal subgroup of | #72242064, #72242070, D13×#1020 |
| maximal normal subgroup of | #72242070, D13×#1020 |
| maximal quotient of | #72259269, #72276058 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1443);