Finite Group Databasebeta

← Prev (#38736187) Next (#38736189) →

C5×Dic139⋊C9 #38736188

order25020
automorphism?
homologyAbelianization (H1) = C4×C5×C9 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic139⋊C9
unambiguous semidirect productDic139⋊(C5×C9)
unambiguous semidirect product(C139⋊C9)⋊(C4×C5)
unambiguous semidirect product(C5×Dic139)⋊C9

Splittings

derived, SylowC139 ⋊ C4×C5×C9
HallC5×C139⋊C9 ⋊ C4
HallC5×Dic139 ⋊ C9
HallC139⋊C9 ⋊ C4×C5
HallC5×C139 ⋊ C4×C9
HallDic139 ⋊ C5×C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D139⋊C3
commutator, hypocenterC139C4×C5×C9
FrattiniC2×C3C5×D139⋊C3
Fitting, socle, prime radicalC2×C3×C5×C139C2×C3
cosocleC2×C3×C139C2×C3×C5
LCSG ▷ C139
UCSC1 ◁ C2×C3×C5

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 25020

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25020, 10);