Finite Group Databasebeta

C2×#23765752 #34446473

order20224
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#23765752

Splittings

FittingC2×C4×C22⋊C4×C79 ⋊ C2
SylowC79 ⋊ C2×#2273

Subgroups

subgroupG/H
centerC24C23×D79
commutatorC2×C79C23×C42
FrattiniC23C24×D79
FittingC2×C4×C22⋊C4×C79C2
socleC24×C79C24
prime radicalC25×D79C22
cosocleC23×C79C25
hypercenterC2×C4×C22⋊C4D79
hypocenterC79C2×#2273
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

5790 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3256 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 327772);