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C7×Dic7×C11⋊C5 #24924727

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

Aliases

direct productC7×Dic7×C11⋊C5
unambiguous semidirect productC7⋊(C4×C7×C11⋊C5)
unambiguous semidirect product(C11×Dic7)⋊(C5×C7)
unambiguous semidirect product(C7×C11×Dic7)⋊C5

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC2×C7D7×C11⋊C5
commutator, hypocenterC7×C11C4×C5×C7
FrattiniC2C7×D7×C11⋊C5
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

490 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×C11⋊C5×ΓL(1,𝔽8)⋊C4, C11⋊C5×#10596873, C11⋊C5×#10596872, …
maximal normal subgroup ofC7×C11⋊C5×ΓL(1,𝔽8)⋊C4, C11⋊C5×#10596873, C11⋊C5×#10596872, …
maximal quotient ofC3×C7×Dic7×C11⋊C5, C7×C11⋊C5×Dic21

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 40);