Finite Group Databasebeta

C2×#23752227 #34077650

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

Aliases

direct productC2×#23752227

Splittings

FittingC2×#104×C151 ⋊ C2
SylowC151 ⋊ C2×#421

Subgroups

subgroupG/H
centerC2×C4D4×D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
FittingC2×#104×C151C2
socleC22×C151C2×C22⋊C4
prime radicalC2×#41×D151C2
cosocleC2×C4×C151C24
hypercenterC2×#104D151
hypocenterC151C2×#421
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×#104

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4832

Conjugacy classes & character table

2144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 13050);