Finite Group Databasebeta

#428×D151 #34077691

order19328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#428×D151

Splittings

Fitting#428×C151 ⋊ C2
SylowC151 ⋊ C2×#428

Subgroups

subgroupG/H
centerC22C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#428×C151C2
socleC22×C151C22×D4
prime radicalC23×D151D4
cosocleC2×C4×C151C24
hypercenter#428D151
hypocenterC151C2×#428
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4832

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 13091);