Finite Group Databasebeta

← Prev (#37528639) Next (#37528641) →

C52×D3×C11×D7 #37528640

order23100
automorphism?
homologyAbelianization (H1) = C22×C52×C11 · Schur multiplier (H2) = C2×C5

Aliases

direct productC52×D3×C11×D7
unambiguous semidirect product(D3×C7)⋊(C2×C52×C11)
unambiguous semidirect product(C3×D7)⋊(C2×C52×C11)
unambiguous semidirect productD21⋊(C2×C52×C11)

Splittings

Fitting, socle, HallC3×C52×C7×C11 ⋊ C22
derived, HallC3×C7 ⋊ C22×C52×C11
HallC52×C7×C11 ⋊ C2×D3
HallC3×C52×C11 ⋊ C2×D7
HallC3×C52×C7 ⋊ C22×C11
HallC3×C7×C11 ⋊ C22×C52
HallC52×C7 ⋊ C2×D3×C11
HallC7×C11 ⋊ C2×C52×D3
HallC3×C52 ⋊ C2×C11×D7
HallC3×C11 ⋊ C2×C52×D7
SylowC7 ⋊ C2×C52×D3×C11
SylowC3 ⋊ C2×C52×C11×D7

Subgroups

subgroupG/H
center, hypercenterC52×C11D3×D7
commutator, cosocle, hypocenterC3×C7C22×C52×C11
FrattiniC1G
Fitting, socleC3×C52×C7×C11C22
LCSG ▷ C3×C7
UCSC1 ◁ C52×C11

320 conjugacy classes of subgroups; only the 160 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 160 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

4125 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 451);