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ΓL(1,𝔽8)×Dic377 #44539744

order31668
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)×Dic377

Splittings

derived, HallC7×C13×C29 ⋊ C3×C4
HallC7×Dic377 ⋊ C3
HallC13×ΓL(1,𝔽8)×C29 ⋊ C4
HallΓL(1,𝔽8)×C29 ⋊ Dic13
HallC13×C29 ⋊ C4×ΓL(1,𝔽8)
HallC13×ΓL(1,𝔽8) ⋊ Dic29
HallC7×C29 ⋊ C3×Dic13
HallC7×C13 ⋊ C3×Dic29
SylowC29 ⋊ ΓL(1,𝔽8)×Dic13
SylowC13 ⋊ ΓL(1,𝔽8)×Dic29
SylowC7 ⋊ C3×Dic377

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×D377
commutator, hypocenterC7×C13×C29C3×C4
Fitting, socle, cosocleC2×C7×C13×C29C2×C3
prime radicalC2×C13×ΓL(1,𝔽8)×C29C2
LCSG ▷ C7×C13×C29
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10556

Conjugacy classes & character table

1900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31668, 39);