Finite Group Databasebeta

#135×#90673 #28407324

order14464
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#135×#90673

Splittings

Fitting#135×C113 ⋊ C4
SylowC113 ⋊ C4×#135

Subgroups

subgroupG/H
centerC4D4×#90673
commutatorC4×C113C23×C4
FrattiniC4C23×#90673
Fitting#135×C113C4
socleC2×C113C2×C4×D4
prime radical#135×D113C2
cosocleC4×D113C24
hypercenter#135#90673
hypocenterC113C4×#135
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C2×C4 ◁ #135

500 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1808

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14464, 21260);