Finite Group Databasebeta

D23×#344 #15673137

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

Aliases

direct productD23×#344

Splittings

FittingC23×#344 ⋊ C2
SylowC23 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D23
commutatorC22×C23C2×C42
FrattiniC22×C4C22×D23
FittingC23×#344C2
socleC2×C23C2×#95
prime radicalC23×D23C2×C4
cosocleC22×C4×C23C23
hypercenter#344D23
hypocenterC23C2×#344
LCSG ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 368

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 4250);