Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#3866)⋊C4 |
| Fitting | C2×C4×C37 ⋊ C4 |
| Sylow | C37 ⋊ #95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×#3866 |
| commutator | C2×C37 | C42 |
| Fitting | C2×C4×C37 | C4 |
| socle | C22×C37 | C2×C4 |
| prime radical, cosocle | C22×D37 | C22 |
| hypercenter | C2×C4 | #3866 |
| hypocenter | C37 | #95 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 296 |
Polycyclic presentation:
2^5,37|a^2=d,b^2=e,b^a=bc,f^a=f^31,f^d=f^3692 conjugacy classes — view the full character table.
| maximal subgroup of | #14558384, #14558385, #14558386, … |
| maximal normal subgroup of | #14558384, #14558385, #14558386, … |
| maximal quotient of | (C2×#3866)⋊C8, #14558399, #14558400, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 197);