Finite Group Databasebeta

#339×Dic67 #30761002

order17152
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C22×C42

Aliases

direct product#339×Dic67

Splittings

SylowC67 ⋊ C4×#339

Subgroups

subgroupG/H
centerC22×C4D4×D67
commutatorC4×C67C43
FrattiniC23×C4C22×D67
FittingC2×#339×C67C2
socleC23×C67C2×C22⋊C4
prime radicalC24×C67C2×D4
cosocleC23×C4×C67C23
hypercenterC2×#339D67
hypocenterC67C4×#339
LCSG ▷ C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#339

1214 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

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, 74739);