Finite Group Databasebeta

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D5×C11×#4294 #34037837

order18810
automorphism?
homologyAbelianization (H1) = C2×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productD5×C11×#4294
unambiguous semidirect productC5⋊(C2×C11×#4294)

Splittings

derived, HallC5×C19 ⋊ C2×C9×C11
HallC5×C11×#4294 ⋊ C2
HallD5×C11×C19 ⋊ C9
HallC5×C11×C19 ⋊ C2×C9
HallC5×#4294 ⋊ C2×C11
HallC11×C19 ⋊ C9×D5
HallD5×C19 ⋊ C9×C11
HallC5×C11 ⋊ C2×#4294
SylowC19 ⋊ C9×D5×C11
SylowC5 ⋊ C2×C11×#4294

Subgroups

subgroupG/H
center, hypercenterC3×C11D5×C19⋊C3
commutator, hypocenterC5×C19C2×C9×C11
FrattiniC3D5×C11×C19⋊C3
Fitting, socleC3×C5×C11×C19C2×C3
prime radicalC3×D5×C11×C19C3
cosocleC3×C5×C19C2×C3×C11
LCSG ▷ C5×C19
UCSC1 ◁ C3×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9405

Conjugacy classes & character table

1188 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×#4294⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)×#4294, C11⋊(#4294⋊AGL(1,𝔽5)), …
maximal normal subgroup ofC11×#4294⋊AGL(1,𝔽5), C11×AGL(1,𝔽5)×#4294, C11⋊(#4294⋊AGL(1,𝔽5)), …
maximal quotient ofC11×Dic5×#4294, C2×D5×C11×#4294

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 30);