Finite Group DatabasebetaFinite Group Databasebeta| order | 1168 |
| isoclinism | isoclinic class of #64408 |
| automorphism | ? |
| homology | Abelianization (H1) = C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C73 ⋊ C16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C4 | #64408 |
| commutator, hypocenter | C73 | C16 |
| Fitting | C4×C73 | C4 |
| socle, prime radical | C2×C73 | C8 |
| cosocle | #10596831 | C2 |
| LCS | G ▷ C73 | |
| UCS | C1 ◁ C4 | |
10 conjugacy classes of subgroups.
| minimal degree | μ(G) = 89 |
| transitive degree | μt(G) = 1168 |
Polycyclic presentation:
2^4,73|a^2=b,b^2=c,c^2=d,e^a=e^27,e^b=e^7288 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11924031, #14556664, #14556665, … |
| maximal normal subgroup of | C2×#11924031, #14556664, #14556665, … |
| maximal quotient of | #14556641, C2×#11924031 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1168, 43);