Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | Q8×C13 ⋊ Dic3 |
| derived | C13×SL(2,𝔽3) ⋊ C4 |
| Sylow | C13 ⋊ #859 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | A4⋊#261 |
| commutator, hypocenter | C13×SL(2,𝔽3) | C4 |
| Fitting | Q8×C13 | Dic3 |
| socle | C2×C13 | SL(2,ℤ/4) |
| prime radical, cosocle | SL(2,𝔽3)×D13 | C2 |
| LCS | G ▷ C13×SL(2,𝔽3) | |
| UCS | C1 ◁ C2 | |
56 conjugacy classes of subgroups.
| transitive degree | μt(G) = 104 |
Polycyclic presentation:
2^2,3,13,2^3|a^2=b,e^2=g,f^2=g,c^a=c^2,d^a=d^8,e^a=ef,f^a=fg,d^b=d^12,e^c=f,f^c=efg,f^e=fg37 conjugacy classes — view the full character table.
| maximal subgroup of | #72259496, #72259501, GL(2,𝔽3)×#261 |
| maximal normal subgroup of | #72259501, GL(2,𝔽3)×#261 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1153);