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C11×ΓL(1,𝔽8)⋊Dic35 #44568502

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)⋊Dic35
unambiguous semidirect productΓL(1,𝔽8)⋊(C11×Dic35)

Splittings

derived, HallC5×C72 ⋊ C3×C4×C11
HallC11×C7⋊Dic35 ⋊ C3
HallC5×C7×C11×ΓL(1,𝔽8) ⋊ C4
HallC5×C72×C11 ⋊ C3×C4
HallC7×C11×ΓL(1,𝔽8) ⋊ Dic5
HallC7⋊Dic35 ⋊ C3×C11
HallC5×C7×ΓL(1,𝔽8) ⋊ C4×C11
HallC72×C11 ⋊ C3×Dic5
HallC7×ΓL(1,𝔽8) ⋊ C11×Dic5
HallC5×C11 ⋊ ΓL(1,𝔽8)⋊Dic7
SylowC72 ⋊ C3×C11×Dic5
SylowC5 ⋊ C11×ΓL(1,𝔽8)⋊Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C11C5⋊(ΓL(1,𝔽8)⋊D7)
commutator, hypocenterC5×C72C3×C4×C11
FrattiniC2C11×C5⋊(ΓL(1,𝔽8)⋊D7)
Fitting, socleC2×C5×C72×C11C2×C3
prime radicalC2×C5×C7×C11×ΓL(1,𝔽8)C2
cosocleC2×C5×C72C2×C3×C11
LCSG ▷ C5×C72
UCSC1 ◁ C2×C11

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

2024 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 204);