Finite Group Databasebeta

← Prev (#14511065) Next (#14511067) →

C2×C5×#5395 #14511066

order1920
isoclinismisoclinic class of #5386
automorphism?
homologyAbelianization (H1) = C23×C5 · Schur multiplier (H2) = C23

Aliases

direct productC2×C5×#5395

Splittings

FittingC2×C4×C5×Q8 ⋊ D3

Subgroups

subgroupG/H
center, socleC23×C5C2×S4
commutator, cosocleC2×SL(2,𝔽3)C23×C5
FrattiniC22C22×C5×S4
FittingC2×C4×C5×Q8D3
prime radicalC22×C5×GL(2,𝔽3)C2
hypercenterC22×C4×C5S4
hypocenterSL(2,𝔽3)C2×C5×D4
LCSG ▷ C2×SL(2,𝔽3) ▷ SL(2,𝔽3)
UCSC1 ◁ C23×C5 ◁ C22×C4×C5

610 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 610 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

230 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236764);