Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| isoclinism | isoclinic class of #90773 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D232 |
| Fitting | C2×C8×C29 ⋊ C2 |
| Sylow | C29 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D116 |
| commutator, cosocle | C4×C29 | C23 |
| Frattini | C4 | C22×D29 |
| Fitting | C2×C8×C29 | C2 |
| socle | C22×C29 | D4 |
| hypercenter | C2×C8 | D29 |
| hypocenter | C29 | C2×D8 |
| LCS | G ▷ C4×C29 ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
238 conjugacy classes — view the full character table.
| maximal subgroup of | #14270963, #14270965, #14270975, … |
| maximal normal subgroup of | #14270963, #14270965, #14270975, … |
| maximal quotient of | C2×#11745169, C2×#11745166, C4×D232, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 124);