Finite Group Databasebeta

C2×(C2×D79)⋊#95 #34209357

order20224
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C210

Aliases

direct productC2×(C2×D79)⋊#95

Splittings

FittingC22×#95×C79 ⋊ C2
SylowC79 ⋊ C2×C22⋊#95

Subgroups

subgroupG/H
centerC25C22×D79
commutatorC22×C79C22×C42
FrattiniC24C23×D79
FittingC22×#95×C79C2
socleC25×C79C23
prime radicalC25×D79C22
cosocleC24×C79C24
hypercenterC22×#95D79
hypocenterC79C2×C22⋊#95
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C25 ◁ C22×#95

7630 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 90656);