Finite Group Databasebeta

← Prev (#37590015) Next (#37590017) →

C4×ΓL(1,𝔽8)×C293 #37590016

order24612
automorphism?
homologyAbelianization (H1) = C3×C4×C293 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C293
unambiguous semidirect product(C4×C7)⋊(C3×C293)
unambiguous semidirect product(C4×C7×C293)⋊C3

Splittings

Fitting, HallC4×C7×C293 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C293
HallC7×C293 ⋊ C3×C4
HallC4×C7 ⋊ C3×C293

Subgroups

subgroupG/H
center, hypercenterC4×C293ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C293
FrattiniC2C2×ΓL(1,𝔽8)×C293
FittingC4×C7×C293C3
socleC2×C7×C293C2×C3
prime radicalC2×ΓL(1,𝔽8)×C293C2
cosocleC2×C7C2×C3×C293
LCSG ▷ C7
UCSC1 ◁ C4×C293

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8204

Conjugacy classes & character table

5860 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24612, 2);