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C5×C3⋊((C31⋊C3)⋊C4) #19150080

order5580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C3⋊((C31⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C5×(C31⋊C3)⋊C4)
unambiguous semidirect product(C5×Dic93)⋊C3

Splittings

derivedC3×C31 ⋊ C3×C4×C5
HallC3×C5×C31⋊C3 ⋊ C4
HallC3×C31⋊C3 ⋊ C4×C5
HallC5×C31 ⋊ C3×Dic3
SylowC31 ⋊ C3×C5×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D31⋊C3)
commutator, hypocenterC3×C31C3×C4×C5
FrattiniC2C5×C3⋊(D31⋊C3)
Fitting, socleC2×C3×C5×C31C2×C3
LCSG ▷ C3×C31
UCSC1 ◁ C2×C5

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

240 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3⋊(((C31⋊C3)⋊C4)⋊C25), C25×C3⋊((C31⋊C3)⋊C4), C5×C3⋊(((C31⋊C3)⋊C4)⋊C5), …
maximal normal subgroup ofC3⋊(((C31⋊C3)⋊C4)⋊C25), C25×C3⋊((C31⋊C3)⋊C4), C5×C3⋊(((C31⋊C3)⋊C4)⋊C5), …
maximal quotient ofC25×C3⋊((C31⋊C3)⋊C4), C52×C3⋊((C31⋊C3)⋊C4), C5×C3⋊((C31⋊C3)⋊Dic5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5580, 69);