Finite Group Databasebeta

C2×C4×#14579137 #34446713

order20224
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×C4×#14579137

Splittings

FittingC22×C4×Q8×C79 ⋊ C2
SylowC79 ⋊ C2×C4×C22⋊Q8

Subgroups

subgroupG/H
centerC23×C4C22×D79
commutatorC22×C79C24×C4
FrattiniC23C24×D79
FittingC22×C4×Q8×C79C2
socleC24×C79C24
prime radicalC24×D79C23
cosocleC23×C79C25
hypercenterC22×C4×Q8D79
hypocenterC79C2×C4×C22⋊Q8
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C23×C4 ◁ C22×C4×Q8

3854 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

3232 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 328012);