Finite Group Databasebeta

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C22×C4×D5×C11 #13183426

order1760
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C23×C4×C11 · Schur multiplier (H2) = C26

Aliases

direct productC22×C4×D5×C11

Splittings

FittingC22×C4×C5×C11 ⋊ C2
derived, SylowC5 ⋊ C23×C4×C11
HallC5×C11 ⋊ C23×C4

Subgroups

subgroupG/H
center, hypercenterC22×C4×C11D5
commutator, hypocenterC5C23×C4×C11
FrattiniC2C23×D5×C11
FittingC22×C4×C5×C11C2
socleC23×C5×C11C22
prime radicalC23×D5×C11C2
cosocleC2×C5C24×C11
LCSG ▷ C5
UCSC1 ◁ C22×C4×C11

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 880

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1760, 1235);