Finite Group Databasebeta

← Prev (#19150076) Next (#19150078) →

C3×C5×(C31⋊C3)⋊C4 #19150077

order5580
isoclinismisoclinic class of D31⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C5 · Schur multiplier (H2) = C3

Aliases

direct productC3×C5×(C31⋊C3)⋊C4
unambiguous semidirect product(C5×Dic31)⋊C32
unambiguous semidirect product(C3×C5×Dic31)⋊C3

Splittings

derived, SylowC31 ⋊ C32×C4×C5
HallC3×C5×C31⋊C3 ⋊ C4
HallC5×Dic31 ⋊ C32
HallC3×C31⋊C3 ⋊ C4×C5
HallC5×C31 ⋊ C32×C4
HallDic31 ⋊ C32×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D31⋊C3
commutator, hypocenterC31C32×C4×C5
FrattiniC2C3×C5×D31⋊C3
Fitting, socleC2×C3×C5×C31C2×C3
LCSG ▷ C31
UCSC1 ◁ C2×C3×C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

330 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×((C31⋊C3)⋊C4)⋊C25, C3×C25×(C31⋊C3)⋊C4, C3×C5×((C31⋊C3)⋊C4)⋊C5, …
maximal normal subgroup ofC3×((C31⋊C3)⋊C4)⋊C25, C3×C25×(C31⋊C3)⋊C4, C3×C5×((C31⋊C3)⋊C4)⋊C5, …
maximal quotient ofC3×C25×(C31⋊C3)⋊C4, C3×C52×(C31⋊C3)⋊C4, C3×C5×(C31⋊C3)⋊Dic5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 66);