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C3×C5×C7⋊(Dic11⋊C5) #37528338

order23100
automorphism?
homologyAbelianization (H1) = C3×C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC3×C5×C7⋊(Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C3×C5×Dic7)
unambiguous semidirect product(C3×Dic77)⋊C52
unambiguous semidirect product(C3×C5×Dic77)⋊C5

Splittings

derived, HallC7×C11 ⋊ C3×C4×C52
HallC3×C5×C7×C11⋊C5 ⋊ C4
HallC5×C7×C11⋊C5 ⋊ C3×C4
HallC3×Dic77 ⋊ C52
HallC3×C5×C11⋊C5 ⋊ Dic7
HallDic77 ⋊ C3×C52
HallC5×C11⋊C5 ⋊ C3×Dic7
HallC3×C7×C11 ⋊ C4×C52
HallC3×C11 ⋊ C52×Dic7
HallC3×C7 ⋊ C5×Dic11⋊C5
SylowC11 ⋊ C3×C52×Dic7
SylowC7 ⋊ C3×C5×Dic11⋊C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C3×C4×C52
FrattiniC2C3×C5×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C5×C7×C11C2×C5
prime radicalC2×C3×C5×C7×C11⋊C5C2
cosocleC2×C7×C11C2×C3×C52
LCSG ▷ C7×C11
UCSC1 ◁ C2×C3×C5

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 149);