Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C24×C13 ⋊ D3 |
| Sylow | C13 ⋊ GL(2,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×A4⋊D13 |
| commutator, cosocle | C2×A4×C13 | C22 |
| Fitting | C24×C13 | D3 |
| socle | C23×C13 | C2×D3 |
| hypercenter | C22 | A4⋊D13 |
| hypocenter | A4×C13 | D4 |
| LCS | G ▷ C2×A4×C13 ▷ A4×C13 | |
| UCS | C1 ◁ C2 ◁ C22 | |
124 conjugacy classes of subgroups; only the 21 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 21 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 156 |
Polycyclic presentation:
2^3,3,13,2^2|b^a=bc,d^a=d^2,e^a=e^12,f^a=fg,f^d=g,g^d=fg110 conjugacy classes — view the full character table.
| maximal subgroup of | #72242064, #72242067, D13×GL(2,ℤ/4) |
| maximal normal subgroup of | #72242067, D13×GL(2,ℤ/4) |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1241);