Finite Group Databasebeta

C2×(C22⋊D139)⋊C8 #31815074

order17792
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×(C22⋊D139)⋊C8

Splittings

FittingC2×C22⋊C8×C139 ⋊ C2
SylowC139 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D139
commutatorC2×C139C23×C8
FrattiniC2×C4C23×D139
FittingC2×C22⋊C8×C139C2
socleC23×C139C22×C4
prime radicalC22×C22⋊D139C4
cosocleC2×C4×C139C24
hypercenterC2×C22⋊C8D139
hypocenterC139C2×C8×D4
LCSG ▷ C2×C139 ▷ C139
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8896

Conjugacy classes & character table

2840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 13180);