Finite Group Databasebeta

C2×#23751974 #34068823

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

Aliases

direct productC2×#23751974

Splittings

SylowC151 ⋊ C2×#340

Subgroups

subgroupG/H
centerC24C22⋊D151
commutatorC4×C151C2×C42
FrattiniC22×C4C22×D151
FittingC22×C4⋊C4×C151C2
socle, prime radicalC24×C151D4
cosocleC22×C4×C151C23
hypercenterC22×C4⋊C4D151
hypocenterC151C2×#340
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C24 ◁ C23×C4 ◁ C22×C4⋊C4

512 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19328

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 4223);