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D7×D15×C11⋊C5 #37528453

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

Aliases

direct productD7×D15×C11⋊C5
unambiguous semidirect product(C3×D7)⋊(D5×C11⋊C5)
unambiguous semidirect product(C5×D7)⋊(D3×C11⋊C5)
unambiguous semidirect product(C11×D7×D15)⋊C5

Splittings

Fitting, socle, derivedC3×C5×C7×C11 ⋊ C22×C5
HallC3×C5×C7×C11⋊C5 ⋊ C22
HallC5×C7×C11⋊C5 ⋊ C2×D3
HallC3×C5×C11⋊C5 ⋊ C2×D7
HallC5×C11⋊C5 ⋊ D3×D7
HallC3×C7×C11 ⋊ C2×C5×D5
HallC7×C11 ⋊ C2×C5×D15
HallC3×C11 ⋊ C5×D5×D7
HallC3×C7 ⋊ C2×D5×C11⋊C5
SylowC11 ⋊ C5×D7×D15
SylowC7 ⋊ C2×D15×C11⋊C5
SylowC3 ⋊ D5×D7×C11⋊C5

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC3×C5×C7×C11C22×C5
LCSG ▷ C3×C5×C7×C11
UCSC1

192 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 48 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) = 1155

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 264);