Finite Group Databasebeta

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D7×D1155 #44568874

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

Aliases

direct productD7×D1155
unambiguous semidirect product(C3×D7)⋊D385
unambiguous semidirect product(C5×D7)⋊D231
unambiguous semidirect product(C7×D7)⋊D165
unambiguous semidirect product(C11×D7)⋊D105

Splittings

Fitting, socle, derived, 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 ⋊ D72
HallC3×C72 ⋊ C2×D55
HallC5×C11 ⋊ D7×D21
SylowC72 ⋊ C2×D165
HallC3×C11 ⋊ D7×D35
HallC3×C5 ⋊ D7×D77
SylowC11 ⋊ D7×D105
SylowC5 ⋊ D7×D231
SylowC3 ⋊ D7×D385

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C72×C11C22
LCSG ▷ C3×C5×C72×C11
UCSC1

208 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 52 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

2895 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 576);