Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | #64408 |
| commutator, hypocenter | C73 | C2×C8 |
| Frattini | C2 | C2×#64408 |
| Fitting | C4×C73 | C4 |
| socle | C2×C73 | C2×C4 |
| prime radical | C2×D73 | C4 |
| cosocle | Dic73 | C22 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C4 | |
22 conjugacy classes of subgroups.
| transitive degree | μt(G) = 584 |
Polycyclic presentation:
2^4,73|a^2=c,c^2=d,e^a=e^27,e^b=e^72,e^c=e^7288 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#64408, #14556645, #14556653, … |
| maximal normal subgroup of | C8×#64408, #14556645, #14556653, … |
| maximal quotient of | C4×#10596833, #14556648, #14556658, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 48);