Finite Group Databasebeta

C2×#20294782 #28362732

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productC2×#20294782

Splittings

SylowC109 ⋊ C2×H(3,ℤ/4)

Subgroups

subgroupG/H
centerC2×C4C4×Dic109
commutatorC4×C109C2×C42
FrattiniC22×C4C22×D109
FittingC2×#117×C109C2
socleC22×C109#95
prime radicalC24×C109D4
cosocleC22×C4×C109C23
hypercenterC2×#117D109
hypocenterC109C2×H(3,ℤ/4)
LCSG ▷ C4×C109 ▷ C109
UCSC1 ◁ C2×C4 ◁ C2×#117

404 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3488

Conjugacy classes & character table

2204 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 4210);