Finite Group Databasebeta

D4×#14268626 #28393471

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD4×#14268626

Splittings

SylowC113 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D113
commutatorC22×C113C23×C4
FittingC2×C4×D4×C113C2
socle, cosocleC23×C113C24
prime radicalC22×D4×C113C22
hypercenterC2×C4×D4D113
hypocenterC113D4×C4⋊C4
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C23 ◁ C2×C4×D4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2290 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 7407);