Finite Group Databasebeta

C2×#23762215 #34257657

order20224
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#23762215

Splittings

FittingC2×Q8⋊C8×C79 ⋊ C2
SylowC79 ⋊ C2×SD16⋊C8

Subgroups

subgroupG/H
centerC22×C4D4×D79
commutatorC4×C79C23×C8
FrattiniC42C23×D79
FittingC2×Q8⋊C8×C79C2
socleC23×C79C4×D4
prime radicalC22×D316C2×C4
cosocleC42×C79C24
hypercenterC2×Q8⋊C8D79
hypocenterC79C2×SD16⋊C8
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

2272 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 138956);