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Dic3×ΓL(1,𝔽8)×C127 #44544747

order32004
automorphism?
homologyAbelianization (H1) = C3×C4×C127 · Schur multiplier (H2) = C1

Aliases

direct productDic3×ΓL(1,𝔽8)×C127
unambiguous semidirect productC3⋊(C4×ΓL(1,𝔽8)×C127)
unambiguous semidirect product(C7×Dic3)⋊(C3×C127)

Splittings

derivedC3×C7 ⋊ C3×C4×C127
HallC3×ΓL(1,𝔽8)×C127 ⋊ C4
HallC7×C127 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C127
SylowC7 ⋊ C3×Dic3×C127

Subgroups

subgroupG/H
center, hypercenterC2×C127D3×ΓL(1,𝔽8)
commutator, hypocenterC3×C7C3×C4×C127
FrattiniC2D3×ΓL(1,𝔽8)×C127
Fitting, socleC2×C3×C7×C127C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C127C2
cosocleC2×C3×C7C2×C3×C127
LCSG ▷ C3×C7
UCSC1 ◁ C2×C127

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10668

Conjugacy classes & character table

3810 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32004, 129);