Finite Group Databasebeta

C2×C4×(C2×D23)⋊C4 #15675728

order2944
isoclinismisoclinic class of Dic46
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D23)⋊C4

Splittings

FittingC22×C42×C23 ⋊ C2
SylowC23 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D23
commutatorC2×C23C22×C42
FrattiniC23C23×D23
FittingC22×C42×C23C2
socleC24×C23C23
prime radicalC24×D23C22
cosocleC23×C23C24
hypercenterC22×C42D23
hypocenterC23C2×C4×C22⋊C4
LCSG ▷ C2×C23 ▷ C23
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1472

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 6841);