Finite Group Databasebeta

#117×#90673 #28407007

order14464
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×#90673

Splittings

Fitting#117×C113 ⋊ C4
SylowC113 ⋊ C4×#117

Subgroups

subgroupG/H
centerC2×C4C22×#90673
commutatorC2×C113C22×C42
FrattiniC22C23×#90673
Fitting#117×C113C4
socleC22×C113C23×C4
prime radicalC23×D113C23
cosocleC22×D113C24
hypercenter#117#90673
hypocenterC113C4×#117
LCSG ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ #117

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 20943);