Finite Group Databasebeta

#376×D113 #28392899

order14464
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#376×D113

Splittings

Fitting#376×C113 ⋊ C2
SylowC113 ⋊ C2×#376

Subgroups

subgroupG/H
centerC22×C4C22×D113
commutatorC2×C113C22×C42
FrattiniC23C23×D113
Fitting#376×C113C2
socle, cosocleC23×C113C24
prime radicalC23×D113C23
hypercenter#376D113
hypocenterC113C2×#376
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C22×C4 ◁ #376

840 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

2320 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6835);