Finite Group Databasebeta

← Prev (#45688560) Next (#45688562) →

C4×ΓL(1,𝔽8)×C397 #45688561

order33348
automorphism?
homologyAbelianization (H1) = C3×C4×C397 · Schur multiplier (H2) = C1

Aliases

direct productC4×ΓL(1,𝔽8)×C397
unambiguous semidirect product(C4×C7)⋊(C3×C397)

Splittings

Fitting, HallC4×C7×C397 ⋊ C3
derived, SylowC7 ⋊ C3×C4×C397
HallC7×C397 ⋊ C3×C4
HallC4×C7 ⋊ C3×C397

Subgroups

subgroupG/H
center, hypercenterC4×C397ΓL(1,𝔽8)
commutator, hypocenterC7C3×C4×C397
FrattiniC2C2×ΓL(1,𝔽8)×C397
FittingC4×C7×C397C3
socleC2×C7×C397C2×C3
prime radicalC2×ΓL(1,𝔽8)×C397C2
cosocleC2×C7C2×C3×C397
LCSG ▷ C7
UCSC1 ◁ C4×C397

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11116

Conjugacy classes & character table

7940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33348, 3);