Finite Group Databasebeta

D23×#421 #15681936

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productD23×#421

Splittings

FittingC23×#421 ⋊ C2
SylowC23 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC23×#421C2
socleC2×C23C22×C22⋊C4
prime radicalC2×#41×D23C2
cosocleC2×C4×C23C24
hypercenter#421D23
hypocenterC23C2×#421
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 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, 13049);