Finite Group Databasebeta

C4×D4×#89137 #28379466

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×D4×#89137

Splittings

FittingC4×D4×C109 ⋊ C4
SylowC109 ⋊ C42×D4

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutatorC2×C109C22×C42
FrattiniC22C23×#89137
FittingC4×D4×C109C4
socleC22×C109C23×C4
prime radicalC2×D4×D109C22
cosocleC22×D109C24
hypercenterC4×D4#89137
hypocenterC109C42×D4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C4×D4

924 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20944);