Finite Group Databasebeta

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C7×C3⋊((C43⋊C3)⋊C4) #24925515

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

Aliases

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

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×C7C3⋊(D43⋊C3)
commutator, hypocenterC3×C43C3×C4×C7
FrattiniC2C7×C3⋊(D43⋊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

420 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 107);