Finite Group DatabasebetaFinite Group Databasebeta| order | 3076 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C769 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C769 | C4 |
| prime radical, cosocle | D769 | C2 |
| LCS | G ▷ C769 | |
| UCS | C1 | |
6 conjugacy classes of subgroups.
| minimal degree | μ(G) = 769 |
| transitive degree | μt(G) = 769 |
Polycyclic presentation:
2^2,769|a^2=b,c^a=c^62,c^b=c^768196 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#15690484, #29506977, #29506978, … |
| maximal normal subgroup of | C5×#15690484, C7×#15690484, C11×#15690484 |
| maximal quotient of | C5×#15690484, #29506977, #29506978, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3076, 3);