Finite Group Databasebeta

#578×D109 #28377794

order13952
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#578×D109

Splittings

Fitting#578×C109 ⋊ C2
SylowC109 ⋊ C2×#578

Subgroups

subgroupG/H
centerC2C22×D4×D109
commutator, cosocleC4×C109C25
FrattiniC4C24×D109
Fitting#578×C109C2
socleC2×C109C23×D4
hypercenter#578D109
hypocenterC109C2×#578
LCSG ▷ C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C2 ◁ #41 ◁ #578

1408 conjugacy classes of subgroups.

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, 19272);