Finite Group Databasebeta

C2×#13092185 #15673132

order2944
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#13092185

Splittings

SylowC23 ⋊ C2×#343

Subgroups

subgroupG/H
centerC23(C2×D23)⋊C4
commutatorC22×C23C2×C42
FrattiniC22×C4C22×D23
FittingC22×M16×C23C2
socleC23×C23C22⋊C4
prime radicalC24×C23C2×C4
cosocleC22×C4×C23C23
hypercenterC22×M16D23
hypocenterC23C2×#343
LCSG ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 4245);