Finite Group Databasebeta

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C11×A4×C197 #39907161

order26004
automorphism?
homologyAbelianization (H1) = C3×C11×C197 · Schur multiplier (H2) = C2

Aliases

direct productC11×A4×C197
unambiguous semidirect productC22⋊(C3×C11×C197)
unambiguous semidirect product(C22×C11)⋊(C3×C197)
unambiguous semidirect product(C22×C197)⋊(C3×C11)
unambiguous semidirect product(C22×C11×C197)⋊C3

Splittings

Fitting, socle, HallC22×C11×C197 ⋊ C3
derived, SylowC22 ⋊ C3×C11×C197
HallC22×C197 ⋊ C3×C11
HallC22×C11 ⋊ C3×C197

Subgroups

subgroupG/H
center, hypercenterC11×C197A4
commutator, cosocle, hypocenterC22C3×C11×C197
FrattiniC1G
Fitting, socleC22×C11×C197C3
LCSG ▷ C22
UCSC1 ◁ C11×C197

20 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8668

Conjugacy classes & character table

8668 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26004, 21);