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C11×ΓL(1,𝔽8)×Dic19 #31798207

order17556
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×Dic19

Splittings

derived, HallC7×C19 ⋊ C3×C4×C11
HallC7×C11×Dic19 ⋊ C3
HallC11×C19×ΓL(1,𝔽8) ⋊ C4
HallC7×C11×C19 ⋊ C3×C4
HallC7×Dic19 ⋊ C3×C11
HallC19×ΓL(1,𝔽8) ⋊ C4×C11
HallC11×C19 ⋊ C4×ΓL(1,𝔽8)
HallC7×C11 ⋊ C3×Dic19
SylowC19 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11×Dic19

Subgroups

subgroupG/H
center, hypercenterC2×C11ΓL(1,𝔽8)×D19
commutator, hypocenterC7×C19C3×C4×C11
FrattiniC2C11×ΓL(1,𝔽8)×D19
Fitting, socleC2×C7×C11×C19C2×C3
prime radicalC2×C11×C19×ΓL(1,𝔽8)C2
cosocleC2×C7×C19C2×C3×C11
LCSG ▷ C7×C19
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5852

Conjugacy classes & character table

1210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 22);