Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C8×C29 ⋊ C4 |
| Sylow | C29 ⋊ #97 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×#1181 |
| commutator, socle | C2×C29 | C42 |
| Fitting | C8×C29 | C4 |
| prime radical | C2×D29 | C2×C4 |
| cosocle | C4×D29 | C22 |
| hypercenter | C8 | #1181 |
| hypocenter | C29 | #97 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C4 ◁ C8 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 232 |
Polycyclic presentation:
2^5,29|a^2=c,b^2=d,d^2=e,b^a=be,f^a=f^12,f^c=f^2876 conjugacy classes — view the full character table.
| maximal subgroup of | #14272053, #14272054, C2×#11745208, … |
| maximal normal subgroup of | #14272053, #14272054, C2×#11745208, … |
| maximal quotient of | #14272004, #6599⋊C8, (C2×#1181)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 67);