Finite Group Databasebeta

← Prev (#34086508) Next (#34086510) →

ΓL(1,𝔽8)⋊C4×C233 #34086509

order19572
automorphism?
homologyAbelianization (H1) = C3×C4×C233 · Schur multiplier (H2) = C1

Aliases

direct productΓL(1,𝔽8)⋊C4×C233
unambiguous semidirect productΓL(1,𝔽8)⋊(C4×C233)
unambiguous semidirect productDic7⋊(C3×C233)
unambiguous semidirect product(Dic7×C233)⋊C3

Splittings

derived, SylowC7 ⋊ C3×C4×C233
HallDic7×C233 ⋊ C3
HallΓL(1,𝔽8)×C233 ⋊ C4
HallC7×C233 ⋊ C3×C4
HallDic7 ⋊ C3×C233
HallΓL(1,𝔽8) ⋊ C4×C233

Subgroups

subgroupG/H
center, hypercenterC2×C233AGL(1,𝔽7)
commutator, hypocenterC7C3×C4×C233
FrattiniC2AGL(1,𝔽7)×C233
Fitting, socleC2×C7×C233C2×C3
prime radicalC2×ΓL(1,𝔽8)×C233C2
cosocleC2×C7C2×C3×C233
LCSG ▷ C7
UCSC1 ◁ C2×C233

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6524

Conjugacy classes & character table

3262 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19572, 11);