Finite Group Databasebeta

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D5×C11×C31⋊C3 #23779476

order10230
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11×C31⋊C3
unambiguous semidirect productC5⋊(C2×C11×C31⋊C3)
unambiguous semidirect product(D5×C31)⋊(C3×C11)
unambiguous semidirect product(D5×C11×C31)⋊C3

Splittings

Fitting, socle, HallC5×C11×C31 ⋊ C2×C3
derived, HallC5×C31 ⋊ C2×C3×C11
HallC5×C11×C31⋊C3 ⋊ C2
HallD5×C11×C31 ⋊ C3
HallC5×C31⋊C3 ⋊ C2×C11
HallC11×C31 ⋊ C3×D5
HallD5×C31 ⋊ C3×C11
HallC5×C11 ⋊ C2×C31⋊C3
SylowC31 ⋊ C3×D5×C11
SylowC5 ⋊ C2×C11×C31⋊C3

Subgroups

subgroupG/H
center, hypercenterC11D5×C31⋊C3
commutator, cosocle, hypocenterC5×C31C2×C3×C11
FrattiniC1G
Fitting, socleC5×C11×C31C2×C3
LCSG ▷ C5×C31
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC11×(C31⋊C3)⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)×C31⋊C3, C11⋊((C31⋊C3)⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC11×(C31⋊C3)⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)×C31⋊C3, C11⋊((C31⋊C3)⋊AGL(1,𝔽5)), …
maximal quotient ofC11×Dic5×C31⋊C3, C2×D5×C11×C31⋊C3, D5×C11×C31⋊C9, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10230, 75);