Finite Group Databasebeta

C5×Q8×C22⋊D5 #13106969

order1600
automorphism?
homologyAbelianization (H1) = C24×C5 · Schur multiplier (H2) = C25

Aliases

direct productC5×Q8×C22⋊D5

Splittings

FittingC22×C52×Q8 ⋊ C2
SylowC52 ⋊ D4×Q8

Subgroups

subgroupG/H
centerC22×C5C23×D5
commutator, cosocleC22×C5C24×C5
FrattiniC22C23×C5×D5
FittingC22×C52×Q8C2
socleC22×C52C24
prime radicalC2×C5×C22⋊D5C22
hypercenterC22×C5×Q8D5
hypocenterC5C5×D4×Q8
LCSG ▷ C22×C5 ▷ C5
UCSC1 ◁ C22×C5 ◁ C22×C5×Q8

716 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 9321);