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C4×C61×C49⋊C3 #49089651

order35868
automorphism?
homologyAbelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1

Aliases

direct productC4×C61×C49⋊C3
unambiguous semidirect product(C4×C49)⋊(C3×C61)

Splittings

Fitting, HallC4×C49×C61 ⋊ C3
derived, SylowC49 ⋊ C3×C4×C61
HallC49×C61 ⋊ C3×C4
HallC4×C49 ⋊ C3×C61

Subgroups

subgroupG/H
center, hypercenterC4×C61C49⋊C3
commutator, hypocenterC49C3×C4×C61
FrattiniC2×C7C2×ΓL(1,𝔽8)×C61
FittingC4×C49×C61C3
socleC2×C7×C61C2×ΓL(1,𝔽8)
prime radicalC2×C61×C49⋊C3C2
cosocleC2×C49C2×C3×C61
LCSG ▷ C49
UCSC1 ◁ C4×C61

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11956

Conjugacy classes & character table

4636 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35868, 3);