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C19×ΓL(1,𝔽8)×Dic11 #31798211

order17556
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC19×ΓL(1,𝔽8)×Dic11
unambiguous semidirect productC11⋊(C4×C19×ΓL(1,𝔽8))
unambiguous semidirect product(C7×Dic11)⋊(C3×C19)

Splittings

derived, HallC7×C11 ⋊ C3×C4×C19
HallC7×C19×Dic11 ⋊ C3
HallC11×C19×ΓL(1,𝔽8) ⋊ C4
HallC7×C11×C19 ⋊ C3×C4
HallC7×Dic11 ⋊ C3×C19
HallC11×ΓL(1,𝔽8) ⋊ C4×C19
HallC11×C19 ⋊ C4×ΓL(1,𝔽8)
HallC7×C19 ⋊ C3×Dic11
SylowC11 ⋊ C4×C19×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C19×Dic11

Subgroups

subgroupG/H
center, hypercenterC2×C19ΓL(1,𝔽8)×D11
commutator, hypocenterC7×C11C3×C4×C19
FrattiniC2C19×ΓL(1,𝔽8)×D11
Fitting, socleC2×C7×C11×C19C2×C3
prime radicalC2×C11×C19×ΓL(1,𝔽8)C2
cosocleC2×C7×C11C2×C3×C19
LCSG ▷ C7×C11
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5852

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17556, 26);