Finite Group Databasebeta

C2×#28380674 #43243634

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

Aliases

direct productC2×#28380674

Splittings

SylowC439 ⋊ C2×#106

Subgroups

subgroupG/H
centerC23C22⋊D439
commutatorC4×C439C22×C4
FrattiniC2×C4C22×D439
FittingC2×C4⋊C4×C439C2
socle, prime radicalC23×C439D4
cosocleC2×C4×C439C23
hypercenterC2×C4⋊C4D439
hypocenterC439C2×#106
LCSG ▷ C4×C439 ▷ C2×C439 ▷ C439
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×C4⋊C4

130 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 28096

Conjugacy classes & character table

4408 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28096, 579);