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C2×C3×C11⋊C5×C97 #44544952

order32010
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C97 · Schur multiplier (H2) = C1

Aliases

direct productC2×C3×C11⋊C5×C97
unambiguous semidirect product(C2×C11)⋊(C3×C5×C97)
unambiguous semidirect product(C2×C3×C11)⋊(C5×C97)
unambiguous semidirect product(C2×C3×C11×C97)⋊C5

Splittings

Fitting, socle, HallC2×C3×C11×C97 ⋊ C5
derived, SylowC11 ⋊ C2×C3×C5×C97
HallC3×C11×C97 ⋊ C2×C5
HallC2×C11×C97 ⋊ C3×C5
HallC11×C97 ⋊ C2×C3×C5
HallC2×C3×C11 ⋊ C5×C97
HallC3×C11 ⋊ C2×C5×C97
HallC2×C11 ⋊ C3×C5×C97

Subgroups

subgroupG/H
center, hypercenterC2×C3×C97C11⋊C5
commutator, cosocle, hypocenterC11C2×C3×C5×C97
FrattiniC1G
Fitting, socleC2×C3×C11×C97C5
LCSG ▷ C11
UCSC1 ◁ C2×C3×C97

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6402

Conjugacy classes & character table

4074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32010, 2);