Finite Group Databasebeta

C2×#28380679 #43243650

order28096
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#28380679

Splittings

SylowC439 ⋊ C2×#108

Subgroups

subgroupG/H
centerC2×C4D1756
commutatorC4×C439C22×C4
FrattiniC2×C4C22×D439
FittingC22×C8×C439C2
socleC22×C439C4⋊C4
prime radicalC23×C439Q8
cosocleC2×C4×C439C23
hypercenterC22×C8D439
hypocenterC439C2×#108
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

7036 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 595);