Finite Group Databasebeta

#1964×D79 #34292010

order20224
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct product#1964×D79

Splittings

FittingC79×#1964 ⋊ C2
SylowC79 ⋊ C2×#1964

Subgroups

subgroupG/H
centerC22C2×C22⋊C4×D79
commutatorC23×C79C23×C4
FrattiniC24C23×D79
FittingC79×#1964C2
socleC22×C79C22×C22⋊C4
prime radicalC2×#121×D79C2
cosocleC24×C79C24
hypercenter#1964D79
hypocenterC79C2×#1964
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

2218 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2528

Conjugacy classes & character table

1312 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 173309);