Finite Group Databasebeta

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C7×Dic3×C43⋊C3 #24925516

order10836
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic3×C43⋊C3
unambiguous semidirect productC3⋊(C4×C7×C43⋊C3)

Splittings

derivedC3×C43 ⋊ C3×C4×C7
HallC3×C7×C43⋊C3 ⋊ C4
HallC3×C43⋊C3 ⋊ C4×C7
HallC7×C43 ⋊ C3×Dic3
SylowC43 ⋊ C3×C7×Dic3

Subgroups

subgroupG/H
center, hypercenterC2×C7D3×C43⋊C3
commutator, hypocenterC3×C43C3×C4×C7
FrattiniC2D3×C7×C43⋊C3
Fitting, socleC2×C3×C7×C43C2×C3
prime radicalC2×C3×C7×C43⋊C3C2
cosocleC2×C3×C43C2×C3×C7
LCSG ▷ C3×C43
UCSC1 ◁ C2×C7

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

714 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 108);