Finite Group Databasebeta

D4×#14523959 #30871177

order17152
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#14523959

Splittings

FittingD4×M16×C67 ⋊ C2
SylowC67 ⋊ D4×#100

Subgroups

subgroupG/H
centerC22C22×(C2×D67)⋊C4
commutatorC23×C67C23×C4
FrattiniC22×C4C23×D67
FittingD4×M16×C67C2
socleC22×C67C22×C22⋊C4
prime radicalC2×D4×D268C2
cosocleC22×C4×C67C24
hypercenterD4×M16D67
hypocenterC67D4×#100
LCSG ▷ C23×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ D4×M16

1862 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

1705 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 184914);