Finite Group Databasebeta

← Prev (#44568951) Next (#44568953) →

C2×C7×D1155 #44568952

order32340
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D1155
unambiguous semidirect product(C2×C3)⋊(C7×D385)
unambiguous semidirect product(C2×C5)⋊(C7×D231)
unambiguous semidirect product(C2×C7)⋊(C7×D165)
unambiguous semidirect product(C2×C11)⋊(C7×D105)

Splittings

Fitting, socleC2×C3×C5×C72×C11 ⋊ C2
derivedC3×C5×C7×C11 ⋊ C22×C7
HallC3×C5×C72×C11 ⋊ C22
HallC5×C72×C11 ⋊ C2×D3
HallC3×C72×C11 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D11
HallC72×C11 ⋊ C2×D15
HallC5×C72 ⋊ C2×D33
HallC3×C5×C11 ⋊ C2×C7×D7
HallC3×C72 ⋊ C2×D55
HallC5×C11 ⋊ C2×C7×D21
SylowC72 ⋊ C2×D165
HallC3×C11 ⋊ C2×C7×D35
HallC3×C5 ⋊ C2×C7×D77
SylowC11 ⋊ C2×C7×D105
SylowC5 ⋊ C2×C7×D231
SylowC3 ⋊ C2×C7×D385

Subgroups

subgroupG/H
center, hypercenterC2×C7D1155
commutator, cosocle, hypocenterC3×C5×C7×C11C22×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C11C2
LCSG ▷ C3×C5×C7×C11
UCSC1 ◁ C2×C7

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

normal subgroups only

This group has 208 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

8106 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 654);