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C19×Dic31⋊C5 #26044516

order11780
automorphism?
homologyAbelianization (H1) = C4×C5×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×Dic31⋊C5
unambiguous semidirect productDic31⋊(C5×C19)
unambiguous semidirect productΓL(1,𝔽32)⋊(C4×C19)
unambiguous semidirect product(C19×Dic31)⋊C5

Splittings

derived, SylowC31 ⋊ C4×C5×C19
HallC19×ΓL(1,𝔽32) ⋊ C4
HallC19×Dic31 ⋊ C5
HallC19×C31 ⋊ C4×C5
HallΓL(1,𝔽32) ⋊ C4×C19
HallDic31 ⋊ C5×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19D31⋊C5
commutator, hypocenterC31C4×C5×C19
FrattiniC2C19×D31⋊C5
Fitting, socleC2×C19×C31C2×C5
prime radicalC2×C19×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C5×C19
LCSG ▷ C31
UCSC1 ◁ C2×C19

24 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C19×Dic31⋊C5, C19×C3⋊(Dic31⋊C5), C19×((C31⋊C3)⋊C4)⋊C5, …
maximal normal subgroup ofC3×C19×Dic31⋊C5, C19×((C31⋊C3)⋊C4)⋊C5, C19⋊C3×Dic31⋊C5, …
maximal quotient ofC3×C19×Dic31⋊C5, C19×C3⋊(Dic31⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11780, 10);