Finite Group DatabasebetaFinite Group Databasebeta| order | 928 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C29 ⋊ C2 |
| Sylow | C29 ⋊ 2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×D29 |
| commutator, socle, cosocle | C2×C29 | C24 |
| Fitting | C2×Q8×C29 | C2 |
| hypercenter | C2×Q8 | D29 |
| hypocenter | C29 | 2−1+4 |
| LCS | G ▷ C2×C29 ▷ C29 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
146 conjugacy classes of subgroups.
| transitive degree | μt(G) = 464 |
Polycyclic presentation:
2^5,29|b^2=e,c^2=e,d^a=de,f^a=f^28,c^b=ce157 conjugacy classes — view the full character table.
| maximal subgroup of | #14271335, #14271338, #14271345, … |
| maximal normal subgroup of | #14271335, #14271338, #14271345, … |
| maximal quotient of | #14271639, #14271641, #14271644, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(928, 221);