Finite Group DatabasebetaFinite Group Databasebeta| order | 17536 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C137 · Schur multiplier (H2) = C29 |
| direct product | C2×#520×C137 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C137 | C24 |
| commutator | C2 | C24×C4×C137 |
| Frattini, cosocle | C22 | C25×C137 |
| prime radical | C22×#41×C137 | C2 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C137 ◁ G | |
1640 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8768 |
9316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C137×#8324, C137×#10765, C137×#10775, … |
| maximal normal subgroup of | C137×#8324, C137×#10765, C137×#10775, … |
| maximal quotient of | C2×#2274×C137, C2×#2275×C137, C2×#2276×C137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(17536, 2159);