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C2×C13⋊C3×C97⋊C3 #36384128

order22698
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC2×C13⋊C3×C97⋊C3
unambiguous semidirect product(C2×C13×C97⋊C3)⋊C3
unambiguous semidirect product(C2×C13⋊C3×C97)⋊C3
unambiguous semidirect product(C2×#16838252)⋊C3
unambiguous semidirect product(C2×#16838253)⋊C3

Splittings

Fitting, socle, HallC2×C13×C97 ⋊ C32
derived, HallC13×C97 ⋊ C2×C32
HallC2×C97 ⋊ C3×C13⋊C3
SylowC97 ⋊ C2×C3×C13⋊C3
HallC2×C13 ⋊ C3×C97⋊C3
SylowC13 ⋊ C2×C3×C97⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C13⋊C3×C97⋊C3
commutator, cosocle, hypocenterC13×C97C2×C32
FrattiniC1G
Fitting, socleC2×C13×C97C32
LCSG ▷ C13×C97
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2522

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22698, 29);