Finite Group Databasebeta

C2×C4×(C2×D139)⋊C4 #31808735

order17792
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D139)⋊C4

Splittings

FittingC22×C42×C139 ⋊ C2
SylowC139 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D139
commutatorC2×C139C22×C42
FrattiniC23C23×D139
FittingC22×C42×C139C2
socleC24×C139C23
prime radicalC24×D139C22
cosocleC23×C139C24
hypercenterC22×C42D139
hypocenterC139C2×C4×C22⋊C4
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8896

Conjugacy classes & character table

4496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 6841);