Finite Group Databasebeta

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D7×D825 #37528291

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

Aliases

direct productD7×D825
unambiguous semidirect product(C3×D7)⋊D275
unambiguous semidirect product(C11×D7)⋊D75
unambiguous semidirect product(D7×C25)⋊D33

Splittings

Fitting, derived, HallC3×C7×C11×C25 ⋊ C22
HallC7×C11×C25 ⋊ C2×D3
HallC3×C11×C25 ⋊ C2×D7
HallC3×C7×C25 ⋊ C2×D11
HallC11×C25 ⋊ D3×D7
HallC3×C7×C11 ⋊ C2×D25
HallC7×C25 ⋊ C2×D33
HallC7×C11 ⋊ C2×D75
HallC3×C25 ⋊ D7×D11
HallC3×C11 ⋊ D7×D25
SylowC25 ⋊ D7×D33
HallC3×C7 ⋊ C2×D275
SylowC11 ⋊ D7×D75
SylowC7 ⋊ C2×D825
SylowC3 ⋊ D7×D275

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC3×C7×C11×C25C22
FrattiniC5D7×D165
socleC3×C5×C7×C11C2×D5
LCSG ▷ C3×C7×C11×C25
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 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) = 5775

Conjugacy classes & character table

2070 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 102);