Finite Group Databasebeta

← Prev (#44568482) Next (#44568484) →

C5×C11⋊(ΓL(1,𝔽8)⋊Dic7) #44568483

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊(ΓL(1,𝔽8)⋊Dic7)
unambiguous semidirect productΓL(1,𝔽8)⋊(C5×Dic77)

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC5×C7⋊Dic77 ⋊ C3
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC7⋊Dic77 ⋊ C3×C5
HallC7×C11×ΓL(1,𝔽8) ⋊ C4×C5
HallC5×C7×ΓL(1,𝔽8) ⋊ Dic11
HallC5×C72 ⋊ C3×Dic11
HallC7×ΓL(1,𝔽8) ⋊ C5×Dic11
HallC5×C11 ⋊ ΓL(1,𝔽8)⋊Dic7
SylowC72 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×ΓL(1,𝔽8)⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊(ΓL(1,𝔽8)⋊D7)
commutator, hypocenterC72×C11C3×C4×C5
FrattiniC2C5×C11⋊(ΓL(1,𝔽8)⋊D7)
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C7×C11×ΓL(1,𝔽8)C2
cosocleC2×C72×C11C2×C3×C5
LCSG ▷ C72×C11
UCSC1 ◁ C2×C5

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

normal subgroups only

This group has 120 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

1970 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 185);