Finite Group Databasebeta

C2×#23761823 #34254661

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

Aliases

direct productC2×#23761823

Splittings

FittingC2×D4⋊C8×C79 ⋊ C2
SylowC79 ⋊ C2×#1486

Subgroups

subgroupG/H
centerC22×C4D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC2×D4⋊C8×C79C2
socleC23×C79C2×C22⋊C4
prime radicalC22×D4×D79C4
cosocleC42×C79C24
hypercenterC2×D4⋊C8D79
hypocenterC79C2×#1486
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×D4⋊C8

1714 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

2260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 135960);