Finite Group Databasebeta

D4×C4⋊#90673 #28407086

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

Aliases

direct productD4×C4⋊#90673

Splittings

FittingC4×D4×C113 ⋊ C4
SylowC113 ⋊ D4×C4⋊C4

Subgroups

subgroupG/H
center, FrattiniC22C23×#90673
commutator, socleC22×C113C23×C4
FittingC4×D4×C113C4
prime radicalC2×D4×D113C22
cosocleC22×D113C24
hypercenterC4×D4#90673
hypocenterC113D4×C4⋊C4
LCSG ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C4×D4

776 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21022);