Finite Group Databasebeta

C2×#23751978 #34068839

order19328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#23751978

Splittings

SylowC151 ⋊ C2×#342

Subgroups

subgroupG/H
centerC23(C2×D151)⋊C4
commutatorC22×C151C2×C42
FrattiniC24C22×D151
FittingC22×C22⋊C4×C151C2
socleC23×C151C22⋊C4
prime radicalC25×C151C22
cosocleC24×C151C23
hypercenterC22×C22⋊C4D151
hypocenterC151C2×#342
LCSG ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C25 ◁ C22×C22⋊C4

680 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4832

Conjugacy classes & character table

3044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 4239);