Finite Group Databasebeta

C2×#23761759 #34254234

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

Aliases

direct productC2×#23761759

Splittings

FittingC22×C22⋊C8×C79 ⋊ C2
SylowC79 ⋊ C2×#1471

Subgroups

subgroupG/H
centerC23C2×(C2×D79)⋊C4
commutatorC23×C79C23×C4
FrattiniC22×C4C23×D79
FittingC22×C22⋊C8×C79C2
socleC23×C79C2×C22⋊C4
prime radicalC22×#14579135C2
cosocleC22×C4×C79C24
hypercenterC22×C22⋊C8D79
hypocenterC79C2×#1471
LCSG ▷ C23×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

1770 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3184 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 135533);