Finite Group Databasebeta

D4×(C2×D23)⋊C4 #15676214

order2944
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productD4×(C2×D23)⋊C4

Splittings

FittingC2×C4×D4×C23 ⋊ C2
SylowC23 ⋊ D4×C22⋊C4

Subgroups

subgroupG/H
center, FrattiniC23C23×D23
commutatorC22×C23C23×C4
FittingC2×C4×D4×C23C2
socle, cosocleC23×C23C24
prime radicalC22×D4×D23C2
hypercenterC2×C4×D4D23
hypocenterC23D4×C22⋊C4
LCSG ▷ C22×C23 ▷ C23
UCSC1 ◁ C23 ◁ C2×C4×D4

1252 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 736

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 7327);