Finite Group DatabasebetaFinite Group Databasebeta| order | 18416 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D4×C1151 ⋊ C2 |
| Sylow | C1151 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D1151 |
| commutator, socle, cosocle | C2×C1151 | C23 |
| Fitting | D4×C1151 | C2 |
| hypercenter | D4 | D1151 |
| hypocenter | C1151 | #41 |
| LCS | G ▷ C2×C1151 ▷ C1151 | |
| UCS | C1 ◁ C2 ◁ D4 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9208 |
Polycyclic presentation:
2^4,1151|c^2=d,b^a=bd,e^c=e^11502885 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49145864, #49145866, #49145869, … |
| maximal normal subgroup of | #49145864, #49145866, #49145869, … |
| maximal quotient of | #49145801, #49145803, (C22⋊D1151)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18416, 39);