Finite Group Databasebeta

← Prev (#41004086) Next (#41004088) →

C3×ΓL(1,𝔽8)⋊C4×C107 #41004087

order26964
automorphism?
homologyAbelianization (H1) = C32×C4×C107 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)⋊C4×C107
unambiguous semidirect productΓL(1,𝔽8)⋊(C3×C4×C107)
unambiguous semidirect productDic7⋊(C32×C107)
unambiguous semidirect product(C3×Dic7)⋊(C3×C107)
unambiguous semidirect product(Dic7×C107)⋊C32
unambiguous semidirect product(C3×Dic7×C107)⋊C3

Splittings

derived, SylowC7 ⋊ C32×C4×C107
HallC3×ΓL(1,𝔽8)×C107 ⋊ C4
HallDic7×C107 ⋊ C32
HallC7×C107 ⋊ C32×C4
HallC3×ΓL(1,𝔽8) ⋊ C4×C107
HallDic7 ⋊ C32×C107

Subgroups

subgroupG/H
center, hypercenterC2×C3×C107AGL(1,𝔽7)
commutator, hypocenterC7C32×C4×C107
FrattiniC2C3×AGL(1,𝔽7)×C107
Fitting, socleC2×C3×C7×C107C2×C3
prime radicalC2×C3×ΓL(1,𝔽8)×C107C2
cosocleC2×C7C2×C32×C107
LCSG ▷ C7
UCSC1 ◁ C2×C3×C107

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8988

Conjugacy classes & character table

4494 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26964, 36);