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C7×C11×C7⋊AGL(1,𝔽5) #24924765

order10780
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

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

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C4
derivedC5×C7 ⋊ C4×C7×C11
HallC72×C11 ⋊ AGL(1,𝔽5)
HallC5×C72 ⋊ C4×C11
HallC5×C11 ⋊ C7×Dic7
SylowC72 ⋊ C11×AGL(1,𝔽5)
SylowC5 ⋊ C7×C11×Dic7

Subgroups

subgroupG/H
center, hypercenterC7×C11C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C4×C7×C11
FrattiniC1G
Fitting, socleC5×C72×C11C4
prime radicalC72×D5×C11C2
cosocleC7×D5C2×C7×C11
LCSG ▷ C5×C7
UCSC1 ◁ C7×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1309 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×#15668773, C7×C11×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C11×ΓL(1,𝔽8)×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC7×C11×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C11×ΓL(1,𝔽8)×C7⋊AGL(1,𝔽5), C11×#15668767, …
maximal quotient ofC3×C7×C11×C7⋊AGL(1,𝔽5), C7×C11×C3⋊(C7⋊AGL(1,𝔽5))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 78);