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C3×(C43⋊C3)⋊Dic7 #24925513

order10836
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×(C43⋊C3)⋊Dic7
unambiguous semidirect product(C43⋊C3)⋊(C3×Dic7)

Splittings

derived, HallC7×C43 ⋊ C32×C4
HallC3×C7×C43⋊C3 ⋊ C4
HallDic301 ⋊ C32
HallC3×C43⋊C3 ⋊ Dic7
SylowC43 ⋊ C32×Dic7
SylowC7 ⋊ C3×(C43⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3(C43⋊C3)⋊D7
commutator, hypocenterC7×C43C32×C4
FrattiniC2C3×(C43⋊C3)⋊D7
Fitting, socleC2×C3×C7×C43C2×C3
prime radicalC2×C3×C7×C43⋊C3C2
cosocleC2×C7×C43C2×C32
LCSG ▷ C7×C43
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

384 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 105);