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C11×C7⋊(C7⋊AGL(1,𝔽5)) #24924767

order10780
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C7

Aliases

direct productC11×C7⋊(C7⋊AGL(1,𝔽5))
unambiguous semidirect productC7⋊(C11×C7⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C4
derived, HallC5×C72 ⋊ C4×C11
HallC72×C11 ⋊ AGL(1,𝔽5)
HallC5×C11 ⋊ C7⋊Dic7
SylowC72 ⋊ C11×AGL(1,𝔽5)
SylowC5 ⋊ C11×C7⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC11C7⋊(C7⋊AGL(1,𝔽5))
commutator, hypocenterC5×C72C4×C11
FrattiniC1G
Fitting, socleC5×C72×C11C4
prime radicalC72×D5×C11C2
cosocleC72×D5C2×C11
LCSG ▷ C5×C72
UCSC1 ◁ C11

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1111 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×ΓL(1,𝔽8)⋊(C7⋊AGL(1,𝔽5)), C11×#15668765, C11×#15668766, …
maximal normal subgroup ofC11×ΓL(1,𝔽8)⋊(C7⋊AGL(1,𝔽5)), C11×#15668765, C11×#15668766, …
maximal quotient ofC3×C11×C7⋊(C7⋊AGL(1,𝔽5)), C11×C3⋊(C7⋊(C7⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 80);