Finite Group DatabasebetaFinite Group Databasebeta| order | 3492 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C97 ⋊ C4 |
| Sylow | C97 ⋊ #157 |
| Sylow | C32 ⋊ #87604 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C97 | C4 |
| prime radical, cosocle | C3⋊D291 | C2 |
| LCS | G ▷ C32×C97 | |
| UCS | C1 | |
20 conjugacy classes of subgroups.
| transitive degree | μt(G) = 582 |
Polycyclic presentation:
2^2,3^2,97|a^2=b,c^a=cd,d^a=cd^2,e^a=e^75,c^b=c^2,d^b=d^2,e^b=e^96222 conjugacy classes — view the full character table.
| maximal subgroup of | C5×#16812840, #31775610, #31775611, … |
| maximal normal subgroup of | C5×#16812840, C7×#16812840, C11×#16812840 |
| maximal quotient of | C5×#16812840, #31775610, #31775611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(3492, 46);