Finite Group Databasebeta

#421×D109 #28371571

order13952
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#421×D109

Splittings

Fitting#421×C109 ⋊ C2
SylowC109 ⋊ C2×#421

Subgroups

subgroupG/H
centerC4C2×D4×D109
commutatorC4×C109C23×C4
FrattiniC2×C4C23×D109
Fitting#421×C109C2
socleC2×C109C22×C22⋊C4
prime radicalC2×#41×D109C2
cosocleC2×C4×C109C24
hypercenter#421D109
hypocenterC109C2×#421
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

772 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1744

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, 13049);