Finite Group DatabasebetaFinite Group Databasebeta| order | 7288 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C4×D911 |
| Fitting | C4×C911 ⋊ C2 |
| derived, Sylow | C911 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C4 | D911 |
| commutator, hypocenter | C911 | C2×C4 |
| Frattini | C2 | C2×D911 |
| Fitting | C4×C911 | C2 |
| socle | C2×C911 | C22 |
| LCS | G ▷ C911 | |
| UCS | C1 ◁ C4 | |
16 conjugacy classes of subgroups.
1828 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×D911, #28410141, C2×C4×D911, … |
| maximal normal subgroup of | C8×D911, #28410141, C2×C4×D911, … |
| maximal quotient of | C4×Dic911, (C2×D911)⋊C4, Dic911⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7288, 7);