Finite Group Databasebeta

C2×#20295992 #28379594

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

Aliases

direct productC2×#20295992

Splittings

FittingC2×M16×C109 ⋊ C4
SylowC109 ⋊ C2×#405

Subgroups

subgroupG/H
centerC2×C4C22×#89137
commutatorC2×C109C22×C42
FrattiniC4C23×#89137
FittingC2×M16×C109C4
socleC22×C109C2×C42
prime radicalC23×D109C2×C4
cosocleC4×D109C24
hypercenterC2×M16#89137
hypocenterC109C2×#405
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×M16

592 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

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, 21072);