Finite Group DatabasebetaFinite Group Databasebeta| order | 1924 |
| isoclinism | isoclinic class of #14515320 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C13×C37 ⋊ C4 |
| Sylow | C37 ⋊ #261 |
| Sylow | C13 ⋊ #3866 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C13×C37 | C4 |
| prime radical, cosocle | D481 | C2 |
| LCS | G ▷ C13×C37 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
| minimal degree | μ(G) = 50 |
| transitive degree | μt(G) = 481 |
Polycyclic presentation:
2^2,13,37|a^2=b,c^a=c^8,d^a=d^31,c^b=c^12,d^b=d^36124 conjugacy classes — view the full character table.
| maximal subgroup of | C7×#14515320, C7⋊#14515320, #31773091, … |
| maximal normal subgroup of | C7×#14515320, C11×#14515320, C13×#14515320, … |
| maximal quotient of | C7×#14515320, C7⋊#14515320, #31773091, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1924, 7);