Finite Group Databasebeta

C2×#28380662 #43243584

order28096
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#28380662

Splittings

SylowC439 ⋊ C2×#101

Subgroups

subgroupG/H
centerC22C22⋊Dic439
commutatorC22×C439C22×C4
FrattiniC2×C4C22×D439
FittingC22×Q8×C439C2
socleC22×C439C22⋊C4
prime radicalC23×C439C2×C4
cosocleC2×C4×C439C23
hypercenterC22×Q8D439
hypocenterC439C2×#101
LCSG ▷ C22×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

146 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14048

Conjugacy classes & character table

4402 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 529);