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C11×#14579424 #43245331

order28182
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#14579424

Splittings

Fitting, socle, HallC7×C11×C61 ⋊ C2×C3
derived, HallC7×C61 ⋊ C2×C3×C11
HallC11×#13046197 ⋊ C2
HallC11×D7×C61 ⋊ C3
Hall#13046197 ⋊ C2×C11
HallD7×C61 ⋊ C3×C11
HallC11×C61 ⋊ AGL(1,𝔽7)
HallC11×D7 ⋊ C61⋊C3
HallC7×C11 ⋊ C2×C61⋊C3
SylowC61 ⋊ C11×AGL(1,𝔽7)
HallD7 ⋊ C11×C61⋊C3
SylowC7 ⋊ C2×C11×C61⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#14579424
commutator, cosocle, hypocenterC7×C61C2×C3×C11
FrattiniC1G
Fitting, socleC7×C11×C61C2×C3
LCSG ▷ C7×C61
UCSC1 ◁ C11

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4697

Conjugacy classes & character table

1177 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28182, 35);