Finite Group Databasebeta

D4×#14524000 #31015227

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

Aliases

direct productD4×#14524000

Splittings

FittingC42×D4×C67 ⋊ C2
SylowC67 ⋊ D4×#117

Subgroups

subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC42×D4×C67C2
socle, cosocleC23×C67C25
prime radicalC22×D4×D67C22
hypercenterC42×D4D67
hypocenterC67D4×#117
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C42×D4

3562 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4288

Conjugacy classes & character table

2740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 328964);