Finite Group Databasebeta

C4×C5×#685 #13102199

order1600
isoclinismisoclinic class of Dic10
automorphism?
homologyAbelianization (H1) = C2×C42×C5 · Schur multiplier (H2) = C23×C4

Aliases

direct productC4×C5×#685

Splittings

FittingC2×C42×C52 ⋊ C2
SylowC52 ⋊ C4×C22⋊C4

Subgroups

subgroupG/H
centerC22×C4×C5C2×D5
commutatorC2×C5C2×C42×C5
FrattiniC23C22×C5×D5
FittingC2×C42×C52C2
socleC23×C52C23
prime radicalC23×C5×D5C22
cosocleC23×C5C23×C5
hypercenterC2×C42×C5D5
hypocenterC5C4×C5×C22⋊C4
LCSG ▷ C2×C5 ▷ C5
UCSC1 ◁ C22×C4×C5 ◁ C2×C42×C5

624 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1600, 4551);