Finite Group Databasebeta

M16×C22⋊D109 #28371766

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productM16×C22⋊D109

Splittings

FittingC22×M16×C109 ⋊ C2
SylowC109 ⋊ D4×M16

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D109
commutator, socleC22×C109C23×C4
FittingC22×M16×C109C2
prime radicalC22×C22⋊D109C4
cosocleC2×C4×C109C24
hypercenterC22×M16D109
hypocenterC109D4×M16
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C22×M16

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 13244);