Finite Group Databasebeta

#99×Dic109 #28362822

order13952
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct product#99×Dic109

Splittings

SylowC109 ⋊ C4×#99

Subgroups

subgroupG/H
centerC22C22⋊C4×D109
commutatorC22×C109C2×C42
FrattiniC24C22×D109
FittingC2×#99×C109C2
socleC22×C109C2×C22⋊C4
prime radicalC22×D4×C109C22
cosocleC24×C109C23
hypercenterC2×#99D109
hypocenterC109C4×#99
LCSG ▷ C22×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

412 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 119 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) = 3488

Conjugacy classes & character table

1232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 4300);