Finite Group DatabasebetaFinite Group Databasebeta| order | 7456 |
| automorphism | ? |
| homology | Abelianization (H1) = C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | C233 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C8 | #11745400 |
| commutator, hypocenter | C233 | C32 |
| Fitting | C8×C233 | C4 |
| socle | C2×C233 | C16 |
| LCS | G ▷ C233 | |
| UCS | C1 ◁ C8 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,233|a^2=b,b^2=c,c^2=d,d^2=e,f^a=f^144,f^b=f^232496 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21418585, #28417366, #28417367, … |
| maximal normal subgroup of | C2×#21418585, #28417366, #28417367, … |
| maximal quotient of | #28417274, C2×#21418585 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7456, 196);