Finite Group Databasebeta

#435×D139 #31815079

order17792
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#435×D139

Splittings

Fitting#435×C139 ⋊ C2
SylowC139 ⋊ C2×#435

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D139
commutator, socleC22×C139C23×C4
Fitting#435×C139C2
prime radicalC2×D4×D139C4
cosocleC2×C4×C139C24
hypercenter#435D139
hypocenterC139C2×#435
LCSG ▷ C22×C139 ▷ C139
UCSC1 ◁ C2×C4 ◁ #435

564 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4448

Conjugacy classes & character table

1988 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17792, 13185);