Finite Group Databasebeta

← Prev (#44531256) Next (#44531258) →

ΓL(1,𝔽8)⋊C4×C373 #44531257

order31332
automorphism?
homologyAbelianization (H1) = C3×C4×C373 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C373
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C373)
unambiguous semidirect productDic7⋊(C3×C373)

Splittings

derived, SylowC7 ⋊ C3×C4×C373
HallDic7×C373 ⋊ C3
HallΓL(1,𝔽8)×C373 ⋊ C4
HallC7×C373 ⋊ C3×C4
HallDic7 ⋊ C3×C373
HallΓL(1,𝔽8) ⋊ C4×C373

Subgroups

subgroupG/H
center, hypercenterC2×C373AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C373
FrattiniC2AGL(1,𝔽7)×C373
Fitting, socleC2×C7×C373C2×C3
prime radicalC2×ΓL(1,𝔽8)×C373C2
cosocleC2×C7C2×C3×C373
LCSG ▷ C7
UCSC1 ◁ C2×C373

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10444

Conjugacy classes & character table

5222 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31332, 18);