Finite Group Databasebeta

C2×C22⋊C8×D131 #30674391

order16768
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D131

Splittings

FittingC2×C22⋊C8×C131 ⋊ C2
SylowC131 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D131
commutatorC2×C131C23×C8
FrattiniC2×C4C23×D131
FittingC2×C22⋊C8×C131C2
socleC23×C131C22×C4
prime radicalC24×D131C4
cosocleC2×C4×C131C24
hypercenterC2×C22⋊C8D131
hypocenterC131C22×C22⋊C8
LCSG ▷ C2×C131 ▷ C131
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4192

Conjugacy classes & character table

2680 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16768, 12940);