Finite Group Databasebeta

C2×C8×#11929625 #35152702

order20224
automorphism?
homologyAbelianization (H1) = C24×C8 · Schur multiplier (H2) = C29

Aliases

direct productC2×C8×#11929625

Splittings

FittingC2×C8×Q8×C79 ⋊ C2
SylowC79 ⋊ C2×C8×#41

Subgroups

subgroupG/H
centerC22×C8C22×D79
commutatorC2×C79C24×C8
FrattiniC2×C4C24×D79
FittingC2×C8×Q8×C79C2
socleC23×C79C23×C4
prime radicalC22×#11929625C4
cosocleC2×C4×C79C25
hypercenterC2×C8×Q8D79
hypocenterC79C2×C8×#41
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C8 ◁ C2×C8×Q8

2566 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

3280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 1034001);