Finite Group Databasebeta

C2×#41×Dic151 #34082292

order19328
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#41×Dic151

Splittings

SylowC151 ⋊ C2×C4×#41

Subgroups

subgroupG/H
centerC22×C4C22×D151
commutatorC2×C151C24×C4
FrattiniC22C24×D151
Fitting, prime radicalC22×#41×C151C2
socleC23×C151C24
cosocleC22×C151C25
hypercenterC22×#41D151
hypocenterC151C2×C4×#41
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C22×#41

1728 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

3080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 17692);