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C43×Dic7⋊C9 #24925422

order10836
isoclinismisoclinic class of AGL(1,𝔽7)
automorphism?
homologyAbelianization (H1) = C4×C9×C43 · Schur multiplier (H2) = C1

Aliases

direct productC43×Dic7⋊C9
unambiguous semidirect productDic7⋊(C9×C43)
unambiguous semidirect product(C7⋊C9)⋊(C4×C43)

Splittings

derived, SylowC7 ⋊ C4×C9×C43
HallC43×C7⋊C9 ⋊ C4
HallDic7×C43 ⋊ C9
HallC7×C43 ⋊ C4×C9
HallC7⋊C9 ⋊ C4×C43
HallDic7 ⋊ C9×C43

Subgroups

subgroupG/H
center, hypercenterC2×C3×C43AGL(1,𝔽7)
commutator, hypocenterC7C4×C9×C43
FrattiniC2×C3AGL(1,𝔽7)×C43
Fitting, socle, prime radicalC2×C3×C7×C43C2×C3
cosocleC2×C3×C7C2×C3×C43
LCSG ▷ C7
UCSC1 ◁ C2×C3×C43

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1806 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 14);