Finite Group DatabasebetaFinite Group Databasebeta| order | 1184 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D8×C37 ⋊ C2 |
| Sylow | C37 ⋊ D16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | #10596939 |
| commutator, cosocle | C8×C37 | C22 |
| Frattini | C8 | C2×D37 |
| Fitting | D8×C37 | C2 |
| socle | C2×C37 | D8 |
| hypercenter | D8 | D37 |
| hypocenter | C37 | D16 |
| LCS | G ▷ C8×C37 ▷ C4×C37 ▷ C2×C37 ▷ C37 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D8 | |
28 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 592 |
Polycyclic presentation:
2^5,37|c^2=de,d^2=e,b^a=bc,c^a=cd,d^a=de,c^b=cd,d^b=de,f^b=f^36137 conjugacy classes — view the full character table.
| maximal subgroup of | D16×D37, C2×#11924477, #14557963, … |
| maximal normal subgroup of | D16×D37, C2×#11924477, #14557963, … |
| maximal quotient of | #14557333, #14557334, #14557358, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1184, 87);