Finite Group Databasebeta

← Prev (#24924725) Next (#24924727) →

C7×C7⋊(Dic11⋊C5) #24924726

order10780
automorphism?
homologyAbelianization (H1) = C4×C5×C7 · Schur multiplier (H2) = C1

Aliases

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

Splittings

derivedC7×C11 ⋊ C4×C5×C7
HallC72×C11⋊C5 ⋊ C4
HallC7×Dic77 ⋊ C5
HallC72×C11 ⋊ C4×C5
HallC11⋊C5 ⋊ C7×Dic7
SylowC72 ⋊ Dic11⋊C5
SylowC11 ⋊ C5×C7×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C7C7⋊AGL(1,𝔽11)
commutator, hypocenterC7×C11C4×C5×C7
FrattiniC2C7×C7⋊AGL(1,𝔽11)
Fitting, socleC2×C72×C11C2×C5
prime radicalC2×C72×C11⋊C5C2
cosocleC2×C7×C11C2×C5×C7
LCSG ▷ C7×C11
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

448 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×ΓL(1,𝔽8)⋊(Dic11⋊C5), (C11⋊C5)⋊#10596873, (C11⋊C5)⋊#10596872, …
maximal normal subgroup ofC7×ΓL(1,𝔽8)⋊(Dic11⋊C5), (C11⋊C5)⋊#10596873, (C11⋊C5)⋊#10596872, …
maximal quotient ofC3×C7×C7⋊(Dic11⋊C5), C7×C3⋊(C7⋊(Dic11⋊C5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 39);