Finite Group Databasebeta

C4×M16×D109 #28371437

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×M16×D109

Splittings

FittingC4×M16×C109 ⋊ C2
SylowC109 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC42C22×D109
commutatorC2×C109C22×C42
FrattiniC2×C4C23×D109
FittingC4×M16×C109C2
socleC22×C109C23×C4
prime radicalC23×D109C2×C4
cosocleC2×C4×C109C24
hypercenterC4×M16D109
hypocenterC109C2×C4×M16
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C42 ◁ C4×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 12915);