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C5×C7⋊(Dic11⋊C5) #21440375

order7700
automorphism?
homologyAbelianization (H1) = C4×C52 · Schur multiplier (H2) = C5

Aliases

direct productC5×C7⋊(Dic11⋊C5)
unambiguous semidirect productC7⋊(C5×Dic11⋊C5)
unambiguous semidirect product(C11⋊C5)⋊(C5×Dic7)
unambiguous semidirect productDic77⋊C52
unambiguous semidirect product(C5×Dic77)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C5C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C4×C52
FrattiniC2C5×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C5×C7×C11C2×C5
LCSG ▷ C7×C11
UCSC1 ◁ C2×C5

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

320 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 39);