Finite Group Databasebeta

C2×C4×(C2×D167)⋊C4 #36326469

order21376
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D167)⋊C4

Splittings

FittingC22×C42×C167 ⋊ C2
SylowC167 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D167
commutatorC2×C167C22×C42
FrattiniC23C23×D167
FittingC22×C42×C167C2
socleC24×C167C23
prime radicalC24×D167C22
cosocleC23×C167C24
hypercenterC22×C42D167
hypocenterC167C2×C4×C22⋊C4
LCSG ▷ C2×C167 ▷ C167
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10688

Conjugacy classes & character table

5392 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21376, 6841);