Finite Group Databasebeta

C2×C4×C4⋊Dic151 #34071445

order19328
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC2×C4×C4⋊Dic151

Splittings

SylowC151 ⋊ C2×C4×C4⋊C4

Subgroups

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

928 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19328

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, 6845);