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ΓL(1,𝔽8)⋊C4×C347 #44415330

order29148
automorphism?
homologyAbelianization (H1) = C3×C4×C347 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C347
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C347)
unambiguous semidirect productDic7⋊(C3×C347)
unambiguous semidirect product(Dic7×C347)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C347
HallDic7×C347 ⋊ C3
HallΓL(1,𝔽8)×C347 ⋊ C4
HallC7×C347 ⋊ C3×C4
HallDic7 ⋊ C3×C347
HallΓL(1,𝔽8) ⋊ C4×C347

Subgroups

subgroupG/H
center, hypercenterC2×C347AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C347
FrattiniC2AGL(1,𝔽7)×C347
Fitting, socleC2×C7×C347C2×C3
prime radicalC2×ΓL(1,𝔽8)×C347C2
cosocleC2×C7C2×C3×C347
LCSG ▷ C7
UCSC1 ◁ C2×C347

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9716

Conjugacy classes & character table

4858 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(29148, 11);