Finite Group Databasebeta

← Prev (#37567817) Next (#37567819) →

C4×ΓL(1,𝔽8)×C97⋊C3 #37567818

order24444
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC4×ΓL(1,𝔽8)×C97⋊C3
unambiguous semidirect product(C4×C7×C97⋊C3)⋊C3
unambiguous semidirect product(C4×ΓL(1,𝔽8)×C97)⋊C3
unambiguous semidirect product(C4×#14523271)⋊C3
unambiguous semidirect product(C4×#14523272)⋊C3

Splittings

Fitting, HallC4×C7×C97 ⋊ C32
derived, HallC7×C97 ⋊ C32×C4
HallC4×C97 ⋊ C3×ΓL(1,𝔽8)
SylowC97 ⋊ C3×C4×ΓL(1,𝔽8)
HallC4×C7 ⋊ C3×C97⋊C3
SylowC7 ⋊ C3×C4×C97⋊C3

Subgroups

subgroupG/H
center, hypercenterC4ΓL(1,𝔽8)×C97⋊C3
commutator, hypocenterC7×C97C32×C4
FrattiniC2C2×ΓL(1,𝔽8)×C97⋊C3
FittingC4×C7×C97C32
socle, cosocleC2×C7×C97C2×C32
prime radicalC2×ΓL(1,𝔽8)×C97⋊C3C2
LCSG ▷ C7×C97
UCSC1 ◁ C4

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2716

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24444, 81);