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Dic3×ΓL(1,𝔽8)×C61 #29506792

order15372
automorphism?
homologyAbelianization (H1) = C3×C4×C61 · Schur multiplier (H2) = C1

Aliases

direct productDic3×ΓL(1,𝔽8)×C61
unambiguous semidirect productC3⋊(C4×ΓL(1,𝔽8)×C61)
unambiguous semidirect product(C7×Dic3)⋊(C3×C61)

Splittings

derivedC3×C7 ⋊ C3×C4×C61
HallC3×ΓL(1,𝔽8)×C61 ⋊ C4
HallC7×C61 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C61
SylowC7 ⋊ C3×Dic3×C61

Subgroups

subgroupG/H
center, hypercenterC2×C61D3×ΓL(1,𝔽8)
commutator, hypocenterC3×C7C3×C4×C61
FrattiniC2D3×ΓL(1,𝔽8)×C61
Fitting, socleC2×C3×C7×C61C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C61C2
cosocleC2×C3×C7C2×C3×C61
LCSG ▷ C3×C7
UCSC1 ◁ C2×C61

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5124

Conjugacy classes & character table

1830 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15372, 102);