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C2×C11×C22⋊Dic5 #13183165

order1760
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C22×C4×C11 · Schur multiplier (H2) = C24

Aliases

direct productC2×C11×C22⋊Dic5

Splittings

HallC5×C11 ⋊ C2×C22⋊C4
SylowC5 ⋊ C2×C11×C22⋊C4

Subgroups

subgroupG/H
centerC23×C11C2×D5
commutatorC2×C5C22×C4×C11
FrattiniC22C22×D5×C11
Fitting, prime radicalC24×C5×C11C2
socleC23×C5×C11C22
cosocleC22×C5C23×C11
hypercenterC24×C11D5
hypocenterC5C2×C11×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C11 ◁ C24×C11

264 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 880

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 974);