Finite Group DatabasebetaFinite Group Databasebeta| order | 6152 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C769 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #15690484 |
| commutator, hypocenter | C769 | C8 |
| Fitting, socle | C2×C769 | C4 |
| LCS | G ▷ C769 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,769|a^2=b,b^2=c,d^a=d^62,d^b=d^768392 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#20259677, #27134389, #27134390, … |
| maximal normal subgroup of | C2×#20259677, #27134389, #27134390, … |
| maximal quotient of | #27134384, C2×#20259677 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6152, 13);