Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#90809 |
| Fitting | C2×Q8×C29 ⋊ C2 |
| Sylow | C29 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D29 |
| commutator, cosocle | C2×C29 | C24 |
| Frattini | C2 | C23×D29 |
| Fitting | C2×Q8×C29 | C2 |
| socle | C22×C29 | C23 |
| hypercenter | C2×Q8 | D29 |
| hypocenter | C29 | C2×#41 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
164 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
160 conjugacy classes — view the full character table.
| maximal subgroup of | #14271146, #14271158, #14271163, … |
| maximal normal subgroup of | #14271146, #14271158, #14271163, … |
| maximal quotient of | C2×#11745254, C2×#11745255, C2×Q8×Dic29, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 220);