Finite Group Databasebeta

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C2×C5×C11×#4296 #34037875

order18810
automorphism?
homologyAbelianization (H1) = C2×C5×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C11×#4296

Splittings

Fitting, socle, HallC2×C5×C11×C19 ⋊ C9
derived, SylowC19 ⋊ C2×C5×C9×C11
HallC5×C11×C19 ⋊ C2×C9
HallC2×C11×C19 ⋊ C5×C9
HallC11×C19 ⋊ C2×C5×C9
HallC2×C5×C19 ⋊ C9×C11
HallC5×C19 ⋊ C2×C9×C11
HallC2×C19 ⋊ C5×C9×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11#4296
commutator, hypocenterC19C2×C5×C9×C11
FrattiniC1G
Fitting, socleC2×C5×C11×C19C9
prime radicalC2×C5×C11×C19⋊C3C3
cosocleC19⋊C3C2×C3×C5×C11
LCSG ▷ C19
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2090

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×#4296⋊C4, C5×C11⋊(#4296⋊C4), C5×Dic11×#4296, …
maximal normal subgroup ofC5×C11×#4296⋊C4, C5×C11⋊(#4296⋊C4), C5×Dic11×#4296, …
maximal quotient ofC4×C5×C11×#4296, C22×C5×C11×#4296

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18810, 68);