Finite Group DatabasebetaFinite Group Databasebeta| order | 18736 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C1171 ⋊ C2 |
| Sylow | C1171 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D1171 |
| commutator, socle, cosocle | C2×C1171 | C23 |
| Frattini | C2 | C22×D1171 |
| Fitting | C2×C4×C1171 | C2 |
| hypercenter | C2×C4 | D1171 |
| hypocenter | C1171 | #41 |
| LCS | G ▷ C2×C1171 ▷ C1171 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9368 |
Polycyclic presentation:
2^4,1171|c^2=d,b^a=bd,e^b=e^11704690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49153984, #49153986, #49154064, … |
| maximal normal subgroup of | #49153984, #49153986, #49154064, … |
| maximal quotient of | #49154015, #49154017, C4×C22⋊D1171, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18736, 40);