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C2×C11⋊C5×C97⋊C3 #44544954

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

Aliases

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

Splittings

Fitting, socle, HallC2×C11×C97 ⋊ C3×C5
derived, HallC11×C97 ⋊ C2×C3×C5
HallC2×C11⋊C5×C97 ⋊ C3
HallC2×C11×C97⋊C3 ⋊ C5
HallC11⋊C5×C97 ⋊ C2×C3
HallC11×C97⋊C3 ⋊ C2×C5
HallC2×C97 ⋊ C3×C11⋊C5
SylowC97 ⋊ C2×C3×C11⋊C5
HallC2×C11 ⋊ C5×C97⋊C3
SylowC11 ⋊ C2×C5×C97⋊C3

Subgroups

subgroupG/H
center, hypercenterC2C11⋊C5×C97⋊C3
commutator, cosocle, hypocenterC11×C97C2×C3×C5
FrattiniC1G
Fitting, socleC2×C11×C97C3×C5
LCSG ▷ C11×C97
UCSC1 ◁ C2

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2134

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(32010, 4);