Finite Group DatabasebetaFinite Group Databasebeta| order | 1136 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C71 ⋊ C2 |
| Sylow | C71 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D71 |
| commutator, socle | C2×C71 | C2×C4 |
| Fitting | C8×C71 | C2 |
| prime radical | C2×D71 | C4 |
| cosocle | C4×C71 | C22 |
| hypercenter | C8 | D71 |
| hypocenter | C71 | M16 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
| minimal degree | μ(G) = 79 |
| transitive degree | μt(G) = 568 |
Polycyclic presentation:
2^4,71|a^2=c,c^2=d,b^a=bd,e^b=e^70290 conjugacy classes — view the full character table.
| maximal subgroup of | M16×D71, C2×#11765848, #14556134, … |
| maximal normal subgroup of | M16×D71, C2×#11765848, #14556134, … |
| maximal quotient of | #14556038, (C2×D71)⋊C8, Dic71⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1136, 23);