Finite Group Databasebeta

← Prev (#41004089) Next (#41004091) →

C107×C3⋊(ΓL(1,𝔽8)⋊C4) #41004090

order26964
automorphism?
homologyAbelianization (H1) = C3×C4×C107 · Schur multiplier (H2) = C1

Aliases

direct productC107×C3⋊(ΓL(1,𝔽8)⋊C4)
unambiguous semidirect productC3⋊(ΓL(1,𝔽8)⋊C4×C107)
unambiguous semidirect productΓL(1,𝔽8)⋊(Dic3×C107)
unambiguous semidirect productDic21⋊(C3×C107)
unambiguous semidirect product(Dic21×C107)⋊C3

Splittings

derivedC3×C7 ⋊ C3×C4×C107
HallC3×ΓL(1,𝔽8)×C107 ⋊ C4
HallC7×C107 ⋊ C3×Dic3
HallC3×ΓL(1,𝔽8) ⋊ C4×C107
SylowC7 ⋊ C3×Dic3×C107

Subgroups

subgroupG/H
center, hypercenterC2×C107C3⋊AGL(1,𝔽7)
commutator, hypocenterC3×C7C3×C4×C107
FrattiniC2C107×C3⋊AGL(1,𝔽7)
Fitting, socleC2×C3×C7×C107C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C107C2
cosocleC2×C3×C7C2×C3×C107
LCSG ▷ C3×C7
UCSC1 ◁ C2×C107

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8988

Conjugacy classes & character table

2568 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26964, 39);