Finite Group Databasebeta

C2×#13063319 #14583424

order2752
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13063319

Splittings

FittingC2×C42×C43 ⋊ C2
SylowC43 ⋊ C2×#126

Subgroups

subgroupG/H
centerC23C22×D43
commutator, cosocleC22×C43C24
FrattiniC22C23×D43
FittingC2×C42×C43C2
socleC23×C43C23
prime radicalC23×D43C22
hypercenterC2×C42D43
hypocenterC43C2×#126
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42

246 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1074);