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#16811773⋊C3 #23779484

order10230
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#16811773⋊C3

Splittings

Fitting, socle, derived, HallC11×C31 ⋊ C2×C3×C5
Hall#13133722⋊C3 ⋊ C2
Hall#16811773 ⋊ C3
HallC11×D31⋊C3 ⋊ C5
Hall#13133722 ⋊ C2×C3
HallC11×C31⋊C3 ⋊ C2×C5
HallC11×D31 ⋊ C3×C5
HallD31⋊C3 ⋊ C11⋊C5
HallC31⋊C3 ⋊ C2×C11⋊C5
HallD31 ⋊ C3×C11⋊C5
SylowC31 ⋊ C2×C3×C11⋊C5
SylowC11 ⋊ AGL(1,𝔽31)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC11×C31C2×C3×C5
LCSG ▷ C11×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2,3,5,11,31|e^a=e^30,e^b=e^25,d^c=d^4,e^c=e^4

Conjugacy classes & character table

53 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#16811773⋊C2)⋊C3, C2×#16811773⋊C3, C3×#16811773⋊C3, …
maximal normal subgroup of(#16811773⋊C2)⋊C3, C2×#16811773⋊C3, C3×#16811773⋊C3
maximal quotient of#20291872⋊C3, C2×#16811773⋊C3, #16811773⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 83);