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C5×C7×C3⋊(Dic11⋊C5) #37528344

order23100
automorphism?
homologyAbelianization (H1) = C4×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×C3⋊(Dic11⋊C5)
unambiguous semidirect productC3⋊(C5×C7×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C5×C7×Dic3)
unambiguous semidirect productDic33⋊(C52×C7)
unambiguous semidirect product(C5×Dic33)⋊(C5×C7)
unambiguous semidirect product(C7×Dic33)⋊C52
unambiguous semidirect product(C5×C7×Dic33)⋊C5

Splittings

derived, HallC3×C11 ⋊ C4×C52×C7
HallC3×C5×C7×C11⋊C5 ⋊ C4
HallC5×C7×C11⋊C5 ⋊ Dic3
HallC7×Dic33 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ C4×C7
HallC5×C11⋊C5 ⋊ C7×Dic3
HallC3×C7×C11 ⋊ C4×C52
HallDic33 ⋊ C52×C7
HallC7×C11 ⋊ C52×Dic3
HallC3×C7 ⋊ C5×Dic11⋊C5
SylowC11 ⋊ C52×C7×Dic3
SylowC3 ⋊ C5×C7×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7C3⋊AGL(1,𝔽11)
commutator, hypocenterC3×C11C4×C52×C7
FrattiniC2C5×C7×C3⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C3×C11C2×C52×C7
LCSG ▷ C3×C11
UCSC1 ◁ C2×C5×C7

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 155);