Finite Group Databasebeta

← Prev (#24902019) Next (#24902021) →

C17×Dic31⋊C5 #24902020

order10540
automorphism?
homologyAbelianization (H1) = C4×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC17×Dic31⋊C5
unambiguous semidirect productDic31⋊(C5×C17)
unambiguous semidirect productΓL(1,𝔽32)⋊(C4×C17)
unambiguous semidirect product(C17×Dic31)⋊C5

Splittings

derived, SylowC31 ⋊ C4×C5×C17
HallC17×ΓL(1,𝔽32) ⋊ C4
HallC17×Dic31 ⋊ C5
HallC17×C31 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C4×C17
HallDic31 ⋊ C5×C17

Subgroups

subgroupG/H
center, hypercenterC2×C17D31⋊C5
commutator, hypocenterC31C4×C5×C17
FrattiniC2C17×D31⋊C5
Fitting, socleC2×C17×C31C2×C5
prime radicalC2×C17×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C5×C17
LCSG ▷ C31
UCSC1 ◁ C2×C17

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C17×Dic31⋊C5, C17×C3⋊(Dic31⋊C5), C17×((C31⋊C3)⋊C4)⋊C5
maximal normal subgroup ofC3×C17×Dic31⋊C5, C17×((C31⋊C3)⋊C4)⋊C5
maximal quotient ofC3×C17×Dic31⋊C5, C17×C3⋊(Dic31⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10540, 10);