Finite Group Databasebeta

#367×D113 #28392352

order14464
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct product#367×D113

Splittings

Fitting#367×C113 ⋊ C2
SylowC113 ⋊ C2×#367

Subgroups

subgroupG/H
centerC22D8×D113
commutatorC8×C113C22×C4
FrattiniC2×C8C22×D113
Fitting#367×C113C2
socleC22×C113C2×D8
prime radicalC22×D113D8
cosocleC2×C8×C113C23
hypercenter#367D113
hypocenterC113C2×#367
LCSG ▷ C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #367

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7232

Conjugacy classes & character table

1276 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 6288);