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C11×#15690920 #46803151

order34188
automorphism?
homologyAbelianization (H1) = C3×C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#15690920

Splittings

derived, HallC7×C37 ⋊ C3×C4×C11
HallC7×C11×Dic37 ⋊ C3
HallC11×#11715913 ⋊ C4
HallC7×C11×C37 ⋊ C3×C4
HallC11×Dic37 ⋊ ΓL(1,𝔽8)
HallC7×Dic37 ⋊ C3×C11
Hall#11715913 ⋊ C4×C11
HallC11×C37 ⋊ C4×ΓL(1,𝔽8)
HallDic37 ⋊ C11×ΓL(1,𝔽8)
HallC7×C11 ⋊ Dic37⋊C3
SylowC37 ⋊ C4×C11×ΓL(1,𝔽8)
SylowC7 ⋊ C11×Dic37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C11#13095531
commutator, hypocenterC7×C37C3×C4×C11
FrattiniC2C11×#13095531
Fitting, socleC2×C7×C11×C37C2×C3
prime radicalC2×C11×#11715913C2
cosocleC2×C7×C37C2×C3×C11
LCSG ▷ C7×C37
UCSC1 ◁ C2×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11396

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 23);