Finite Group Databasebeta

D4×Q8×D109 #28376502

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productD4×Q8×D109

Splittings

FittingD4×Q8×C109 ⋊ C2
SylowC109 ⋊ C2×D4×Q8

Subgroups

subgroupG/H
center, FrattiniC22C24×D109
commutator, socle, cosocleC22×C109C25
FittingD4×Q8×C109C2
prime radicalC2×D4×D109C22
hypercenterD4×Q8D109
hypocenterC109C2×D4×Q8
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C22 ◁ D4×Q8

1568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

1400 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17980);