Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C37 ⋊ #131 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#3866 |
| commutator, socle | C2×C37 | C22×C4 |
| Fitting | Q8×C37 | C4 |
| prime radical | #10596966 | C2 |
| cosocle | Dic37 | C23 |
| hypercenter | Q8 | #3866 |
| hypocenter | C37 | #131 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ Q8 | |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^5,37|a^2=d,d^2=e,f^a=f^31,c^b=ce,f^b=f^36,f^c=f^36,f^d=f^3665 conjugacy classes — view the full character table.
| maximal subgroup of | #14558576, #14558577, #14558578, … |
| maximal normal subgroup of | #14558576, #14558577, #14558578, … |
| maximal quotient of | #14558498, #14558508, #14558540, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 234);