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Dic3×ΓL(1,𝔽8)×C67 #30683121

order16884
automorphism?
homologyAbelianization (H1) = C3×C4×C67 · Schur multiplier (H2) = C1

Aliases

direct productDic3×ΓL(1,𝔽8)×C67
unambiguous semidirect productC3⋊(C4×ΓL(1,𝔽8)×C67)
unambiguous semidirect product(C7×Dic3)⋊(C3×C67)

Splittings

derivedC3×C7 ⋊ C3×C4×C67
HallC3×ΓL(1,𝔽8)×C67 ⋊ C4
HallC7×C67 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C67
SylowC7 ⋊ C3×Dic3×C67

Subgroups

subgroupG/H
center, hypercenterC2×C67D3×ΓL(1,𝔽8)
commutator, hypocenterC3×C7C3×C4×C67
FrattiniC2D3×ΓL(1,𝔽8)×C67
Fitting, socleC2×C3×C7×C67C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C67C2
cosocleC2×C3×C7C2×C3×C67
LCSG ▷ C3×C7
UCSC1 ◁ C2×C67

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5628

Conjugacy classes & character table

2010 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16884, 90);