Finite Group Databasebeta

C2×SD16×C79⋊C8 #34257633

order20224
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×SD16×C79⋊C8

Splittings

SylowC79 ⋊ C2×C8×SD16

Subgroups

subgroupG/H
centerC22×C4D4×D79
commutatorC4×C79C23×C8
FrattiniC42C23×D79
FittingC2×C4×SD16×C79C2
socleC23×C79C4×D4
prime radicalC22×D4×C79C2×C4
cosocleC42×C79C24
hypercenterC2×C4×SD16D79
hypocenterC79C2×C8×SD16
LCSG ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×SD16

822 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10112

Conjugacy classes & character table

2296 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20224, 138932);