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C7×C7⋊(C11⋊AGL(1,𝔽5)) #24924766

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

Aliases

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

Splittings

Fitting, socle, HallC5×C72×C11 ⋊ C4
derivedC5×C7×C11 ⋊ C4×C7
HallC72×C11 ⋊ AGL(1,𝔽5)
HallC5×C72 ⋊ Dic11
HallC5×C11 ⋊ C7×Dic7
SylowC72 ⋊ C11⋊AGL(1,𝔽5)
SylowC11 ⋊ C7×C7⋊AGL(1,𝔽5)
SylowC5 ⋊ C7×Dic77

Subgroups

subgroupG/H
center, hypercenterC7C7⋊(C11⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C11C4×C7
FrattiniC1G
Fitting, socleC5×C72×C11C4
prime radicalC72×D5×C11C2
cosocleC7×D5×C11C2×C7
LCSG ▷ C5×C7×C11
UCSC1 ◁ C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1099 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 79);