Finite Group Databasebeta

C2×C22⋊Q8×D139 #31819628

order17792
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×C22⋊Q8×D139

Splittings

FittingC2×C22⋊Q8×C139 ⋊ C2
SylowC139 ⋊ C22×C22⋊Q8

Subgroups

subgroupG/H
centerC23C23×D139
commutator, cosocleC22×C139C25
FrattiniC22C24×D139
FittingC2×C22⋊Q8×C139C2
socleC23×C139C24
prime radicalC24×D139C22
hypercenterC2×C22⋊Q8D139
hypocenterC139C22×C22⋊Q8
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

1840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4448

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 17734);