Finite Group Databasebeta

C2×C5×D5×C22⋊C4 #13106639

order1600
automorphism?
homologyAbelianization (H1) = C23×C4×C5 · Schur multiplier (H2) = C27

Aliases

direct productC2×C5×D5×C22⋊C4

Splittings

FittingC2×C52×C22⋊C4 ⋊ C2
SylowC52 ⋊ C22×C22⋊C4

Subgroups

subgroupG/H
centerC23×C5C22×D5
commutatorC2×C5C23×C4×C5
FrattiniC22C23×C5×D5
FittingC2×C52×C22⋊C4C2
socleC23×C52C23
prime radicalC24×C5×D5C2
cosocleC22×C5C24×C5
hypercenterC2×C5×C22⋊C4D5
hypocenterC5C22×C5×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C23×C5 ◁ C2×C5×C22⋊C4

1480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 160

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 8991);