Finite Group Databasebeta

← Prev (#37528347) Next (#37528349) →

C7×C3⋊((C11⋊C5)⋊Dic5) #37528348

order23100
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C3⋊((C11⋊C5)⋊Dic5)
unambiguous semidirect productC3⋊(C7×(C11⋊C5)⋊Dic5)
unambiguous semidirect product(C11⋊C5)⋊(C7×Dic15)
unambiguous semidirect productDic165⋊(C5×C7)
unambiguous semidirect product(C7×Dic165)⋊C5

Splittings

derivedC3×C5×C11 ⋊ C4×C5×C7
HallC3×C5×C7×C11⋊C5 ⋊ C4
HallC5×C7×C11⋊C5 ⋊ Dic3
HallC3×C5×C11⋊C5 ⋊ C4×C7
HallC5×C11⋊C5 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ C5×Dic5
HallC7×C11 ⋊ C5×Dic15
HallC3×C11 ⋊ C5×C7×Dic5
HallC3×C7 ⋊ (C11⋊C5)⋊Dic5
SylowC11 ⋊ C5×C7×Dic15
SylowC3 ⋊ C7×(C11⋊C5)⋊Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C7C3⋊(C5⋊AGL(1,𝔽11))
commutator, hypocenterC3×C5×C11C4×C5×C7
FrattiniC2C7×C3⋊(C5⋊AGL(1,𝔽11))
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C3×C5×C11C2×C5×C7
LCSG ▷ C3×C5×C11
UCSC1 ◁ C2×C7

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

normal subgroups only

This group has 128 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) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 159);