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C11×ΓL(1,𝔽8)×C101 #37552270

order23331
automorphism?
homologyAbelianization (H1) = C3×C11×C101 · Schur multiplier (H2) = C1

Aliases

direct productC11×ΓL(1,𝔽8)×C101
unambiguous semidirect productC7⋊(C3×C11×C101)
unambiguous semidirect product(C7×C11)⋊(C3×C101)
unambiguous semidirect product(C7×C101)⋊(C3×C11)
unambiguous semidirect product(C7×C11×C101)⋊C3

Splittings

Fitting, socle, HallC7×C11×C101 ⋊ C3
derived, SylowC7 ⋊ C3×C11×C101
HallC7×C101 ⋊ C3×C11
HallC7×C11 ⋊ C3×C101

Subgroups

subgroupG/H
center, hypercenterC11×C101ΓL(1,𝔽8)
commutator, cosocle, hypocenterC7C3×C11×C101
FrattiniC1G
Fitting, socleC7×C11×C101C3
LCSG ▷ C7
UCSC1 ◁ C11×C101

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7777

Conjugacy classes & character table

5555 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23331, 2);