Finite Group DatabasebetaFinite Group Databasebeta| order | 1950 |
| isoclinism | isoclinic class of #14519613 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C13 ⋊ C2×C3 |
| Hall | C13×C52⋊C3 ⋊ C2 |
| Hall | C5⋊D65 ⋊ C3 |
| Hall | C52⋊C3 ⋊ D13 |
| Sylow | C52 ⋊ C3×D13 |
| Sylow | C13 ⋊ (C5⋊D5)⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C52×C13 | C2×C3 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 195 |
Polycyclic presentation:
2,3,5^2,13|c^a=c^4,d^a=d^4,e^a=e^12,c^b=cd,d^b=c^2d^376 conjugacy classes — view the full character table.
| maximal subgroup of | #3874⋊D13, #16839106, #16839107, … |
| maximal normal subgroup of | #3874⋊D13, #16839106, #16839107, … |
| maximal quotient of | #16839056, C2×#14519613, C7×#14519613, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1950, 23);