Finite Group Databasebeta

C2×D4×Dic302 #34082584

order19328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×D4×Dic302

Splittings

SylowC151 ⋊ C2×D4×Q8

Subgroups

subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC2×C4×D4×C151C2
socleC23×C151C24
prime radicalC22×D4×C151C22
hypercenterC2×C4×D4D151
hypocenterC151C2×D4×Q8
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×C4×D4

1568 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

3050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 17984);