Finite Group Databasebeta

C22×(C22⋊D131)⋊C4 #30679129

order16768
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×(C22⋊D131)⋊C4

Splittings

FittingC22×C22⋊C4×C131 ⋊ C2
SylowC131 ⋊ C22×C4×D4

Subgroups

subgroupG/H
centerC24C22×D131
commutatorC2×C131C24×C4
FrattiniC22C24×D131
FittingC22×C22⋊C4×C131C2
socleC24×C131C23
prime radicalC23×C22⋊D131C2
cosocleC22×C131C25
hypercenterC22×C22⋊C4D131
hypocenterC131C22×C4×D4
LCSG ▷ C2×C131 ▷ C131
UCSC1 ◁ C24 ◁ C22×C22⋊C4

2528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8384

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, 17678);