Finite Group DatabasebetaFinite Group Databasebeta| order | 2418 |
| isoclinism | isoclinic class of #14559031 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C31 ⋊ C2×C3 |
| Hall | #11925881 ⋊ C2 |
| Hall | D403 ⋊ C3 |
| Sylow | C31 ⋊ D13⋊C3 |
| Sylow | C13 ⋊ D31⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C13×C31 | C2×C3 |
| LCS | G ▷ C13×C31 | |
| UCS | C1 | |
16 conjugacy classes of subgroups.
| minimal degree | μ(G) = 44 |
| transitive degree | μt(G) = 403 |
Polycyclic presentation:
2,3,13,31|c^a=c^12,d^a=d^30,c^b=c^3,d^b=d^573 conjugacy classes — view the full character table.
| maximal subgroup of | #14559023⋊C2, C2×#14559031, C5×#14559031, … |
| maximal normal subgroup of | #14559023⋊C2, C2×#14559031, C5×#14559031, … |
| maximal quotient of | #18012820, C2×#14559031, C5×#14559031, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2418, 24);