Finite Group Databasebeta

D23×#440 #15682172

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

Aliases

direct productD23×#440

Splittings

FittingC23×#440 ⋊ C2
SylowC23 ⋊ C2×#440

Subgroups

subgroupG/H
centerC22C2×D4×D23
commutatorC4×C23C23×C4
FrattiniC2×C4C23×D23
FittingC23×#440C2
socleC22×C23C22×D4
prime radicalC2×D4×D23C22
cosocleC2×C4×C23C24
hypercenter#440D23
hypocenterC23C2×#440
LCSG ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #440

544 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

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, 13285);