Finite Group DatabasebetaFinite Group Databasebeta| order | 1300 |
| isoclinism | isoclinic class of #13049937 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C5 |
No aliases for this group.
| Fitting, socle, derived, Hall | C52×C13 ⋊ C4 |
| Sylow | C52 ⋊ #261 |
| Sylow | C13 ⋊ #1039 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C52×C13 | C4 |
| prime radical, cosocle | C52×D13 | C2 |
| LCS | G ▷ C52×C13 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 325 |
Polycyclic presentation:
2^2,5^2,13|a^2=b,c^a=c^4,d^a=d^4,e^a=e^8,e^b=e^12103 conjugacy classes — view the full character table.
| maximal subgroup of | #16839092, #16839113, #16839115, … |
| maximal normal subgroup of | #16839092, #16839113, #16839115, … |
| maximal quotient of | C3×#13049937, C3⋊#13049937, #26043858, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1300, 39);