Finite Group Databasebeta

C2×C4×#14579118 #34446455

order20224
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×C4×#14579118

Splittings

FittingC2×C43×C79 ⋊ C2
SylowC79 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC22×C42C2×D79
commutatorC2×C79C23×C42
FrattiniC23C24×D79
FittingC2×C43×C79C2
socleC24×C79C24
prime radicalC24×D79C23
cosocleC23×C79C25
hypercenterC2×C43D79
hypocenterC79C2×C4×#117
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C42 ◁ C2×C43

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

5152 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 327754);