Finite Group Databasebeta

#421×D151 #34077649

order19328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#421×D151

Splittings

Fitting#421×C151 ⋊ C2
SylowC151 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting#421×C151C2
socleC2×C151C22×C22⋊C4
prime radicalC2×#41×D151C2
cosocleC2×C4×C151C24
hypercenter#421D151
hypocenterC151C2×#421
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2416

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, 13049);