Finite Group Databasebeta

← Prev (#44568490) Next (#44568492) →

C7×C11⋊(ΓL(1,𝔽8)⋊Dic5) #44568491

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11⋊(ΓL(1,𝔽8)⋊Dic5)
unambiguous semidirect productC11⋊(C7×ΓL(1,𝔽8)⋊Dic5)
unambiguous semidirect productΓL(1,𝔽8)⋊(C7×Dic55)
unambiguous semidirect productDic385⋊(C3×C7)

Splittings

derivedC5×C7×C11 ⋊ C3×C4×C7
HallC7×Dic385 ⋊ C3
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC7×C11×ΓL(1,𝔽8) ⋊ Dic5
HallC5×C7×ΓL(1,𝔽8) ⋊ Dic11
HallC72×C11 ⋊ C3×Dic5
HallC5×C72 ⋊ C3×Dic11
HallC7×ΓL(1,𝔽8) ⋊ Dic55
HallC5×C11 ⋊ C7×ΓL(1,𝔽8)⋊C4
SylowC72 ⋊ C3×Dic55
SylowC11 ⋊ C7×ΓL(1,𝔽8)⋊Dic5
SylowC5 ⋊ C7×C11⋊(ΓL(1,𝔽8)⋊C4)

Subgroups

subgroupG/H
center, hypercenterC2×C7C5⋊(C11⋊AGL(1,𝔽7))
commutator, hypocenterC5×C7×C11C3×C4×C7
FrattiniC2C7×C5⋊(C11⋊AGL(1,𝔽7))
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C7×C11×ΓL(1,𝔽8)C2
cosocleC2×C5×C7×C11C2×C3×C7
LCSG ▷ C5×C7×C11
UCSC1 ◁ C2×C7

104 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 52 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4620

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 193);