Finite Group DatabasebetaFinite Group Databasebeta| order | 7136 |
| isoclinism | isoclinic class of D223 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×D223 |
| Fitting | C2×C8×C223 ⋊ C2 |
| derived, Sylow | C223 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D223 |
| commutator, hypocenter | C223 | C22×C8 |
| Frattini | C4 | C22×D223 |
| Fitting | C2×C8×C223 | C2 |
| socle | C22×C223 | C2×C4 |
| LCS | G ▷ C223 | |
| UCS | C1 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
1808 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D223)⋊C16, C4×C8×D223, #97×D223, … |
| maximal normal subgroup of | (C2×D223)⋊C16, C4×C8×D223, #97×D223, … |
| maximal quotient of | C4×C8×D223, C2×C8×Dic223, C22⋊C8×D223, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7136, 147);