Finite Group Databasebeta

#2190×D71 #32151333

order18176
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#2190×D71

Splittings

FittingC71×#2190 ⋊ C2
SylowC71 ⋊ C2×#2190

Subgroups

subgroupG/H
centerC2#447×D71
commutator, cosocleC2×C8×C71C24
FrattiniC2×C8C23×D71
FittingC71×#2190C2
socleC2×C71C2×#447
hypercenter#2190D71
hypocenterC71C2×#2190
LCSG ▷ C2×C8×C71 ▷ C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2190

1180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1136

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 323449);