Finite Group Databasebeta

C2×C4×(C2×D151)⋊C4 #34071441

order19328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D151)⋊C4

Splittings

FittingC22×C42×C151 ⋊ C2
SylowC151 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D151
commutatorC2×C151C22×C42
FrattiniC23C23×D151
FittingC22×C42×C151C2
socleC24×C151C23
prime radicalC24×D151C22
cosocleC23×C151C24
hypercenterC22×C42D151
hypocenterC151C2×C4×C22⋊C4
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

4880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 6841);