Finite Group Databasebeta

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D5×C11×D105 #37528678

order23100
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productD5×C11×D105
unambiguous semidirect product(C3×D5)⋊(C11×D35)
unambiguous semidirect product(C5×D5)⋊(C11×D21)
unambiguous semidirect product(C7×D5)⋊(C11×D15)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C22
derived, HallC3×C52×C7 ⋊ C22×C11
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC52×C11 ⋊ C2×D21
HallC3×C7×C11 ⋊ D52
HallC52×C7 ⋊ C2×D3×C11
HallC7×C11 ⋊ D5×D15
HallC3×C52 ⋊ C2×C11×D7
HallC3×C11 ⋊ D5×D35
SylowC52 ⋊ C2×C11×D21
HallC3×C7 ⋊ D52×C11
SylowC7 ⋊ D5×C11×D15
SylowC3 ⋊ D5×C11×D35

Subgroups

subgroupG/H
center, hypercenterC11D5×D105
commutator, cosocle, hypocenterC3×C52×C7C22×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C52×C7
UCSC1 ◁ C11

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Conjugacy classes & character table

2376 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 489);