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C5×C7×Dic11⋊C5 #21440374

order7700
isoclinismisoclinic class of AGL(1,𝔽11)
automorphism?
homologyAbelianization (H1) = C4×C52×C7 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7×Dic11⋊C5
unambiguous semidirect productDic11⋊(C52×C7)
unambiguous semidirect product(C11⋊C5)⋊(C4×C5×C7)
unambiguous semidirect product(C5×Dic11)⋊(C5×C7)
unambiguous semidirect product(C7×Dic11)⋊C52
unambiguous semidirect product(C5×C7×Dic11)⋊C5

Splittings

derived, SylowC11 ⋊ C4×C52×C7
HallC5×C7×C11⋊C5 ⋊ C4
HallC7×Dic11 ⋊ C52
HallC5×C11⋊C5 ⋊ C4×C7
HallC7×C11 ⋊ C4×C52
HallDic11 ⋊ C52×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7AGL(1,𝔽11)
commutator, hypocenterC11C4×C52×C7
FrattiniC2C5×C7×AGL(1,𝔽11)
Fitting, socleC2×C5×C7×C11C2×C5
LCSG ▷ C11
UCSC1 ◁ C2×C5×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

770 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×ΓL(1,𝔽8)×Dic11⋊C5, C3×C5×C7×Dic11⋊C5, C5×C7×C3⋊(Dic11⋊C5)
maximal normal subgroup ofC5×ΓL(1,𝔽8)×Dic11⋊C5, C3×C5×C7×Dic11⋊C5
maximal quotient ofC3×C5×C7×Dic11⋊C5, C5×C7×C3⋊(Dic11⋊C5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 38);