Finite Group Databasebeta

← Prev (#28376244) Next (#28376246) →

2−1+4×Dic109 #28376245

order13952
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct product2−1+4×Dic109

Splittings

SylowC109 ⋊ C4×2−1+4

Subgroups

subgroupG/H
center, FrattiniC22C24×D109
commutatorC2×C109C24×C4
Fitting, prime radicalC2×2−1+4×C109C2
socle, cosocleC22×C109C25
hypercenterC2×2−1+4D109
hypocenterC109C4×2−1+4
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C2×2−1+4

1492 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.

normal subgroups only

This group has 1492 conjugacy classes of subgroups — too many to draw. Only its 1063 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) = 6976

Conjugacy classes & character table

1904 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 17723);