Finite Group DatabasebetaFinite Group Databasebeta| order | 7288 |
| automorphism | Aut(G) order 6632080 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D3644 |
| unambiguous semidirect product | C4⋊D911 |
| Fitting | C4×C911 ⋊ C2 |
| Sylow | C911 ⋊ D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D911 |
| commutator, socle | C2×C911 | C22 |
| Fitting | C4×C911 | C2 |
| hypercenter | C4 | D911 |
| hypocenter | C911 | D4 |
| LCS | G ▷ C2×C911 ▷ C911 | |
| UCS | C1 ◁ C2 ◁ C4 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,911|b^a=bc,d^a=d^910,d^b=d^9101825 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #28410143, D7288, #28410145, … |
| maximal normal subgroup of | #28410143, D7288, #28410145, … |
| maximal quotient of | (C2×D911)⋊C4, C4⋊Dic911, D7288, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7288, 10);