Finite Group Databasebeta

C2×#20295909 #28378743

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#20295909

Splittings

FittingC2×M16×C109 ⋊ C4
SylowC109 ⋊ C2×#344

Subgroups

subgroupG/H
centerC22(C2×#89137)⋊C4
commutatorC22×C109C2×C42
FrattiniC2×C4C22×#89137
FittingC2×M16×C109C4
socleC22×C109#95
prime radicalC23×D109C2×C4
cosocleC2×C4×D109C23
hypercenterC2×M16#89137
hypocenterC109C2×#344
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 20221);