Finite Group Databasebeta

D4×#14523971 #30871506

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

Aliases

direct productD4×#14523971

Splittings

FittingC42×D4×C67 ⋊ C2
SylowC67 ⋊ D4×#104

Subgroups

subgroupG/H
centerC2×C4C22×D268
commutatorC2×C4×C67C23×C4
FrattiniC22×C4C23×D67
FittingC42×D4×C67C2
socleC22×C67C22×C22⋊C4
prime radicalD4×#11761628C2
cosocleC22×C4×C67C24
hypercenterC42×D4D67
hypocenterC67D4×#104
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C2×C4 ◁ C2×C4×D4 ◁ C42×D4

1608 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2144

Conjugacy classes & character table

2710 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17152, 185243);