Finite Group Databasebeta

← Prev (#32912058) Next (#32912060) →

C7×C31×ΓL(1,𝔽8)⋊C4 #32912059

order18228
automorphism?
homologyAbelianization (H1) = C3×C4×C7×C31 · Schur multiplier (H2) = C1

Aliases

direct productC7×C31×ΓL(1,𝔽8)⋊C4
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C7×C31)
unambiguous semidirect productDic7⋊(C3×C7×C31)

Splittings

derivedC7 ⋊ C3×C4×C7×C31
HallC7×Dic7×C31 ⋊ C3
HallC7×ΓL(1,𝔽8)×C31 ⋊ C4
HallC72×C31 ⋊ C3×C4
HallC7×Dic7 ⋊ C3×C31
HallC7×ΓL(1,𝔽8) ⋊ C4×C31
SylowC72 ⋊ C3×C4×C31

Subgroups

subgroupG/H
center, hypercenterC2×C7×C31AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C7×C31
FrattiniC2C7×C31×AGL(1,𝔽7)
Fitting, socleC2×C72×C31C2×C3
prime radicalC2×C7×ΓL(1,𝔽8)×C31C2
cosocleC2×C7C2×C3×C7×C31
LCSG ▷ C7
UCSC1 ◁ C2×C7×C31

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2604

Conjugacy classes & character table

3038 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18228, 67);