Finite Group Databasebeta

#376×D109 #28365357

order13952
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#376×D109

Splittings

Fitting#376×C109 ⋊ C2
SylowC109 ⋊ C2×#376

Subgroups

subgroupG/H
centerC22×C4C22×D109
commutatorC2×C109C22×C42
FrattiniC23C23×D109
Fitting#376×C109C2
socle, cosocleC23×C109C24
prime radicalC23×D109C23
hypercenter#376D109
hypocenterC109C2×#376
LCSG ▷ C2×C109 ▷ C109
UCSC1 ◁ C22×C4 ◁ #376

840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6976

Conjugacy classes & character table

2240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13952, 6835);