Finite Group Databasebeta

← Prev (#43248573) Next (#43248575) →

C17×(C139⋊C3)⋊C4 #43248574

order28356
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×(C139⋊C3)⋊C4
unambiguous semidirect product(C139⋊C3)⋊(C4×C17)
unambiguous semidirect productDic139⋊(C3×C17)
unambiguous semidirect product(C17×Dic139)⋊C3

Splittings

derived, SylowC139 ⋊ C3×C4×C17
HallC17×Dic139 ⋊ C3
HallC17×C139⋊C3 ⋊ C4
HallC17×C139 ⋊ C3×C4
HallDic139 ⋊ C3×C17
HallC139⋊C3 ⋊ C4×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D139⋊C3
commutator, hypocenterC139C3×C4×C17
FrattiniC2C17×D139⋊C3
Fitting, socleC2×C17×C139C2×C3
prime radicalC2×C17×C139⋊C3C2
cosocleC2×C139C2×C3×C17
LCSG ▷ C139
UCSC1 ◁ C2×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9452

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28356, 10);