Finite Group DatabasebetaFinite Group Databasebeta| order | 10244 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C197 ⋊ C4 |
| Sylow | C197 ⋊ #261 |
| Sylow | C13 ⋊ #11716161 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C197 | C4 |
| prime radical, cosocle | D2561 | C2 |
| LCS | G ▷ C13×C197 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,13,197|a^2=b,c^a=c^5,d^a=d^14,c^b=c^12,d^b=d^196644 conjugacy classes — view the full character table.
| maximal subgroup of | #23779583⋊C3, C3×#23779583, C3⋊#23779583 |
| maximal normal subgroup of | #23779583⋊C3, C3×#23779583 |
| maximal quotient of | C3×#23779583, C3⋊#23779583 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10244, 9);