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C3×C7×(C43⋊C3)⋊C4 #24925503

order10836
automorphism?
homologyAbelianization (H1) = C32×C4×C7 · Schur multiplier (H2) = C3

Aliases

direct productC3×C7×(C43⋊C3)⋊C4

Splittings

derived, SylowC43 ⋊ C32×C4×C7
HallC3×C7×C43⋊C3 ⋊ C4
HallC7×Dic43 ⋊ C32
HallC3×C43⋊C3 ⋊ C4×C7
HallC7×C43 ⋊ C32×C4
HallDic43 ⋊ C32×C7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D43⋊C3
commutator, hypocenterC43C32×C4×C7
FrattiniC2C3×C7×D43⋊C3
Fitting, socleC2×C3×C7×C43C2×C3
prime radicalC2×C3×C7×C43⋊C3C2
cosocleC2×C43C2×C32×C7
LCSG ▷ C43
UCSC1 ◁ C2×C3×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

546 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10836, 95);