Finite Group Databasebeta

D23×#418 #15681895

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct productD23×#418

Splittings

FittingC23×#418 ⋊ C2
SylowC23 ⋊ C2×#418

Subgroups

subgroupG/H
centerC22C2×D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC23×#418C2
socleC22×C23C22×D4
prime radicalC22×D4×D23C2
cosocleC2×C4×C23C24
hypercenter#418D23
hypocenterC23C2×#418
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

1008 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, 13008);