Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C37 ⋊ M32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#3866 |
| commutator, socle | C2×C37 | C2×C8 |
| Fitting | C2×C4×C37 | C4 |
| prime radical | C22×C37 | C8 |
| cosocle | #64436 | C22 |
| hypercenter | C2×C4 | #3866 |
| hypocenter | C37 | M32 |
| LCS | G ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^5,37|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^31,f^c=f^3692 conjugacy classes — view the full character table.
| maximal subgroup of | #14558425, #14558426, #14558429, … |
| maximal normal subgroup of | #14558425, #14558426, #14558429, … |
| maximal quotient of | #14558421, C22⋊#10596927, C4⋊#10596927, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 220);