Finite Group Databasebeta

C4×#19098579 #34285995

order20224
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#19098579

Splittings

FittingC2×C4×M16×C79 ⋊ C2
SylowC79 ⋊ C4×#421

Subgroups

subgroupG/H
centerC42C2×C22⋊D79
commutatorC4×C79C22×C42
FrattiniC22×C4C23×D79
FittingC2×C4×M16×C79C2
socleC22×C79C22×C22⋊C4
prime radicalC22×#11929624C22
cosocleC22×C4×C79C24
hypercenterC2×C4×M16D79
hypocenterC79C4×#421
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

1618 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5056

Conjugacy classes & character table

3208 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 167294);