Finite Group Databasebeta

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C2×C5×D1155 #37528755

order23100
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D1155
unambiguous semidirect product(C2×C3)⋊(C5×D385)
unambiguous semidirect product(C2×C5)⋊(C5×D231)
unambiguous semidirect product(C2×C7)⋊(C5×D165)

Splittings

Fitting, socleC2×C3×C52×C7×C11 ⋊ C2
derivedC3×C5×C7×C11 ⋊ C22×C5
HallC3×C52×C7×C11 ⋊ C22
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D11
HallC52×C11 ⋊ C2×D21
HallC3×C7×C11 ⋊ C2×C5×D5
HallC52×C7 ⋊ C2×D33
HallC7×C11 ⋊ C2×C5×D15
HallC3×C52 ⋊ C2×D77
HallC3×C11 ⋊ C2×C5×D35
SylowC52 ⋊ C2×D231
HallC3×C7 ⋊ C2×C5×D55
SylowC11 ⋊ C2×C5×D105
SylowC7 ⋊ C2×C5×D165
SylowC3 ⋊ C2×C5×D385

Subgroups

subgroupG/H
center, hypercenterC2×C5D1155
commutator, cosocle, hypocenterC3×C5×C7×C11C22×C5
FrattiniC1G
Fitting, socleC2×C3×C52×C7×C11C2
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C2×C5

192 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 4620

Conjugacy classes & character table

5790 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 566);