Finite Group Databasebeta

C22×#19098410 #34446441

order20224
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C210×C4

Aliases

direct productC22×#19098410

Splittings

FittingC22×#95×C79 ⋊ C2
SylowC79 ⋊ C22×C4×C22⋊C4

Subgroups

subgroupG/H
centerC25C22×D79
commutatorC2×C79C23×C42
FrattiniC23C24×D79
FittingC22×#95×C79C2
socleC25×C79C23
prime radicalC25×D79C22
cosocleC23×C79C25
hypercenterC22×#95D79
hypocenterC79C22×C4×C22⋊C4
LCSG ▷ C2×C79 ▷ C79
UCSC1 ◁ C25 ◁ C22×#95

9534 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

3280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 327740);