Finite Group Databasebeta

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C11×D21⋊D25 #37528306

order23100
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2

Aliases

direct productC11×D21⋊D25
unambiguous semidirect productD21⋊(C11×D25)
unambiguous semidirect productD75⋊(C11×D7)
unambiguous semidirect productD175⋊(D3×C11)

Splittings

Fitting, HallC3×C7×C11×C25 ⋊ C22
derived, HallC3×C7×C25 ⋊ C22×C11
HallC7×C11×C25 ⋊ C2×D3
HallC3×C11×C25 ⋊ C2×D7
HallC11×C25 ⋊ D3×D7
HallC3×C7×C11 ⋊ C2×D25
HallC7×C25 ⋊ C2×D3×C11
HallC7×C11 ⋊ D3×D25
HallC3×C25 ⋊ C2×C11×D7
HallC3×C11 ⋊ D7×D25
SylowC25 ⋊ D3×C11×D7
HallC3×C7 ⋊ C2×C11×D25
SylowC7 ⋊ D3×C11×D25
SylowC3 ⋊ C11×D7×D25

Subgroups

subgroupG/H
center, hypercenterC11D21⋊D25
commutator, cosocle, hypocenterC3×C7×C25C22×C11
FrattiniC5C11×D15⋊D7
FittingC3×C7×C11×C25C22
socleC3×C5×C7×C11C2×D5
LCSG ▷ C3×C7×C25
UCSC1 ◁ C11

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

1749 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 117);