Finite Group Databasebeta

#533×Dic67 #31014375

order17152
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C28

Aliases

direct product#533×Dic67

Splittings

SylowC67 ⋊ C4×#533

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC2×#533×C67C2
socle, cosocleC23×C67C25
prime radicalC24×C67C24
hypercenterC2×#533D67
hypocenterC67C4×#533
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C2×#533

2550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8576

Conjugacy classes & character table

1960 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 328112);