Finite Group DatabasebetaFinite Group Databasebeta| order | 2416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C151 ⋊ C2 |
| Sylow | C151 ⋊ D8 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D151 |
| commutator, cosocle | C4×C151 | C22 |
| Frattini | C4 | C2×D151 |
| Fitting | D4×C151 | C2 |
| socle | C2×C151 | D4 |
| hypercenter | D4 | D151 |
| hypocenter | C151 | D8 |
| LCS | G ▷ C4×C151 ▷ C2×C151 ▷ C151 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ D4 | |
22 conjugacy classes of subgroups.
| minimal degree | μ(G) = 159 |
| transitive degree | μt(G) = 1208 |
Polycyclic presentation:
2^4,151|c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^150382 conjugacy classes — view the full character table.
| maximal subgroup of | D8×D151, C2×#14558989, #18012759, … |
| maximal normal subgroup of | D8×D151, C2×#14558989, #18012759, … |
| maximal quotient of | #18012659, #18012660, #18012672, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2416, 25);