Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| isoclinism | isoclinic class of #1181 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C8×#1181 |
| Fitting | C8×C29 ⋊ C4 |
| derived, Sylow | C29 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | #1181 |
| commutator, hypocenter | C29 | C4×C8 |
| Frattini | C4 | C2×#1181 |
| Fitting | C8×C29 | C4 |
| socle | C2×C29 | C42 |
| prime radical | C2×D29 | C2×C4 |
| cosocle | C4×D29 | C22 |
| LCS | G ▷ C29 | |
| UCS | C1 ◁ C8 | |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
88 conjugacy classes — view the full character table.
| maximal subgroup of | C16×#1181, #14272050, C2×C8×#1181, … |
| maximal normal subgroup of | C16×#1181, #14272050, C2×C8×#1181, … |
| maximal quotient of | C8×#6599, #6599⋊C8, (C2×#1181)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 66);