Finite Group Databasebeta

C22×#10621882 #14583668

order2752
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC22×#10621882

Splittings

FittingC22×D4×C43 ⋊ C2
SylowC43 ⋊ C22×D8

Subgroups

subgroupG/H
centerC23C22⋊D43
commutator, cosocleC4×C43C24
FrattiniC4C23×D43
FittingC22×D4×C43C2
socleC23×C43D4
hypercenterC22×D4D43
hypocenterC43C22×D8
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1376

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2752, 1318);