Finite Group Databasebeta

#1964×D71 #32001193

order18176
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct product#1964×D71

Splittings

FittingC71×#1964 ⋊ C2
SylowC71 ⋊ C2×#1964

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D71
commutatorC23×C71C23×C4
FrattiniC24C23×D71
FittingC71×#1964C2
socleC22×C71C22×C22⋊C4
prime radicalC2×#121×D71C2
cosocleC24×C71C24
hypercenter#1964D71
hypocenterC71C2×#1964
LCSG ▷ C23×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

2218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2272

Conjugacy classes & character table

1184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18176, 173309);