Finite Group Databasebeta

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C2×C5×C4⋊Dic11 #13183052

order1760
isoclinismisoclinic class of Dic22
automorphism?
homologyAbelianization (H1) = C22×C4×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C5×C4⋊Dic11

Splittings

HallC5×C11 ⋊ C2×C4⋊C4
SylowC11 ⋊ C2×C5×C4⋊C4

Subgroups

subgroupG/H
centerC23×C5C2×D11
commutatorC2×C11C22×C4×C5
FrattiniC22C22×C5×D11
FittingC22×C4×C5×C11C2
socle, prime radicalC23×C5×C11C22
cosocleC22×C11C23×C5
hypercenterC22×C4×C5D11
hypocenterC11C2×C5×C4⋊C4
LCSG ▷ C2×C11 ▷ C11
UCSC1 ◁ C23×C5 ◁ C22×C4×C5

184 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1760

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 861);